diff --git a/.coverage b/.coverage
index 7bd62455cae2ec79af9cbc60f552afe43fca17d4..bf1a819edb9c1da044cf1d4a9886dcae9c8a0d44 100644
Binary files a/.coverage and b/.coverage differ
diff --git a/.coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx b/.coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx
new file mode 100644
index 0000000000000000000000000000000000000000..e1f7e6f75f5aa9a7a33884193b67b7cc22082200
Binary files /dev/null and b/.coverage.DESKTOP-ATMEKSV.10052.XHqUUOFx differ
diff --git a/.gitignore b/.gitignore
index 423a52d16b06a08d3f9e81333eb2f10abb2542ab..f2b103b6c11c649eb5891a0430ffd5f2abe8aab2 100644
--- a/.gitignore
+++ b/.gitignore
@@ -27,3 +27,5 @@ examples/*/.ipynb_checkpoints
examples/*/Outputs_*
*/Outputs_*
+# Ignore files for local environments
+*_env/*
diff --git a/Outputs_Bayes_None_Calib/emcee_sampler.h5 b/Outputs_Bayes_None_Calib/emcee_sampler.h5
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diff --git a/docs/diagrams/.$Structure_BayesInf.drawio.bkp b/docs/diagrams/.$Structure_BayesInf.drawio.bkp
new file mode 100644
index 0000000000000000000000000000000000000000..2e28cbcb3f3e16bee1b42a18f2b93c6f73a156f7
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+ <mxCell id="KLYezTmecfuvBG8KQe-n-2" value="" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="170" y="110" width="700" height="220" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-3" value="" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="170" y="370" width="180" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-4" value="" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="170" y="440" width="180" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-5" value="" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="170" y="500" width="180" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-6" value="adaptPlot" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="190" y="150" width="70" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-7" value="apoly_construction" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="280" y="150" width="140" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-8" value="bayes_linear" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="440" y="150" width="90" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-9" value="engine" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="550" y="150" width="70" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-11" value="eval_rec_rule" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="640" y="150" width="100" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-12" value="exp_designs" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="760" y="150" width="90" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-13" value="exploration" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="190" y="210" width="80" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-14" value="glexindex" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="290" y="210" width="70" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-15" value="input_space" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="380" y="210" width="80" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-16" value="inputs" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="480" y="210" width="70" height="50" as="geometry" />
+ </mxCell>
+ <mxCell id="KLYezTmecfuvBG8KQe-n-17" value="meta_model_engine" style="shape=folder;fontStyle=1;spacingTop=10;tabWidth=40;tabHeight=14;tabPosition=left;html=1;whiteSpace=wrap;" parent="1" vertex="1">
+ <mxGeometry x="570" y="210" width="160" height="50" as="geometry" />
+ </mxCell>
+ </root>
+ </mxGraphModel>
+ </diagram>
+</mxfile>
diff --git a/examples/analytical-function/classinteraction.gv b/examples/analytical-function/classinteraction.gv
deleted file mode 100644
index 50824f1f36f0dcb539dc4e8b0f7ed6b70d87c896..0000000000000000000000000000000000000000
--- a/examples/analytical-function/classinteraction.gv
+++ /dev/null
@@ -1,44 +0,0 @@
-digraph classinteraction {
- node [shape=box]
- PyLinkForwardModel
- BayesInference
- BayesModelComparison
- Discrepancy
- MCMC
- PostProcessing
- BayesLinearRegression
- EBLinearRegression
- VBLinearRegression
- Engine
- ExpDesigns
- Exploration
- InputSpace
- Input
- Marginal
- OrthogonalMatchingPursuit
- RegressionFastARD
- RegressionFastLaplace
- MetaModel
- node [shape=ellipse]
- gelman_rubin
- within_range
- adaptPlot
- apoly_construction
- gamma_mean
- hellinger_distance
- logpdf
- subdomain
- eval_rec_rule
- eval_rec_rule_arbitrary
- eval_univ_basis
- poly_rec_coeffs
- check_ranges
- cross_truncate
- glexindex
- corr
- update_precisions
- corr_loocv_error
- create_psi
- gaussian_process_emulator
- Input -> Marginal [label=""]
-}
diff --git a/examples/analytical-function/example_analytical_function.py b/examples/analytical-function/example_analytical_function.py
index bdf22598a0c19b031a8b4bb4196c16744bddae14..09261acba65231d3b9782d06fa10ce8c18a95085 100644
--- a/examples/analytical-function/example_analytical_function.py
+++ b/examples/analytical-function/example_analytical_function.py
@@ -25,15 +25,21 @@ matplotlib.use('agg')
# import bayesvalidrox
# Add BayesValidRox path
+sys.path.append("src/")
sys.path.append("../../src/")
+import bayesvalidrox
+from bayesvalidrox import PyLinkForwardModel
+
from bayesvalidrox.pylink.pylink import PyLinkForwardModel
from bayesvalidrox.surrogate_models.inputs import Input
from bayesvalidrox.surrogate_models.exp_designs import ExpDesigns
from bayesvalidrox.surrogate_models.surrogate_models import MetaModel
+#from bayesvalidrox.surrogate_models.meta_model_engine import MetaModelEngine
from bayesvalidrox.post_processing.post_processing import PostProcessing
from bayesvalidrox.bayes_inference.bayes_inference import BayesInference
from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
+
from bayesvalidrox.surrogate_models.engine import Engine
if __name__ == "__main__":
diff --git a/examples/analytical-function_sequentialdesign/analytical_function.py b/examples/analytical-function_sequentialdesign/analytical_function.py
new file mode 100644
index 0000000000000000000000000000000000000000..c7dfaca489abd3dcd2a147f3192c22af8be0c810
--- /dev/null
+++ b/examples/analytical-function_sequentialdesign/analytical_function.py
@@ -0,0 +1,135 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Wed Nov 20 14:48:43 2019
+
+@author: farid
+"""
+import numpy as np
+import scipy.stats as stats
+import scipy.stats as st
+import seaborn as sns
+
+
+def analytical_function(xx, t=None):
+ """
+ Analytical Non-Gaussian Function
+
+ Authors: Farid Mohammadi, University of Stuttgart
+ Sergey Oladyshkin, University of Stuttgart
+ Questions/Comments: Please email Farid Mohammadi at:
+ farid.mohammadi@iws.uni-stuttgart.de
+
+ For function details and reference information, see:
+ https://doi.org/10.3390/e21111081
+
+ Parameters
+ ----------
+ xx : array
+ [x1, x2, ..., xn] where xn ~ Uinform(-5, 5).
+ t : array, optional
+ vector of times. The default is None. ( k − 1 ) /9 and k = 1,..., 10
+
+ Returns
+ -------
+ array
+ row vector of time vectors (s, t).
+
+ """
+ nParamSets, nParams = xx.shape
+
+ if t is None:
+ t = np.arange(0, 10, 1.) / 9
+
+ term1 = (xx[:, 0]**2 + xx[:, 1] - 1)**2
+
+ term2 = xx[:, 0]**2
+
+ term3 = 0.1 * xx[:, 0] * np.exp(xx[:, 1])
+
+ term5 = 0
+ if nParams > 2:
+ for i in range(2, nParams):
+ term5 = term5 + xx[:, i]**3/i
+
+ const = term1 + term2 + term3 + 1 + term5
+
+ # Compute time dependent term
+ term4 = np.zeros((nParamSets, len(t)))
+ for idx in range(nParamSets):
+ term4[idx] = -2 * xx[idx, 0] * np.sqrt(0.5*t)
+
+ Output = term4 + np.repeat(const[:, None], len(t), axis=1)
+
+ return {'x_values': t, 'Z': Output[0]}
+
+
+if __name__ == "__main__":
+
+ MCSize = 10000
+ ndim = 10
+ sigma = 2
+
+ # -------------------------------------------------------------------------
+ # ----------------------- Synthetic data generation -----------------------
+ # -------------------------------------------------------------------------
+ t = np.arange(0, 10, 1.) / 9
+
+ MAP = np.zeros((1, ndim))
+ synthethicData = analytical_function(MAP, t=t)
+
+ # -------------------------------------------------------------------------
+ # ---------------------- Generate Prior distribution ----------------------
+ # -------------------------------------------------------------------------
+
+ xx = np.zeros((MCSize, ndim))
+
+ params = (-5, 5)
+
+ for idxDim in range(ndim):
+ lower, upper = params
+ xx[:, idxDim] = stats.uniform(
+ loc=lower, scale=upper-lower).rvs(size=MCSize)
+
+ # -------------------------------------------------------------------------
+ # ------------- BME and Kullback-Leibler Divergence -----------------------
+ # -------------------------------------------------------------------------
+ Outputs = analytical_function(xx, t=t)
+
+ cov_matrix = np.diag(np.repeat(sigma**2, synthethicData.shape[1]))
+
+ Likelihoods = st.multivariate_normal.pdf(
+ Outputs['Z'], mean=synthethicData[1], cov=cov_matrix)
+
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
+
+ normLikelihood = Likelihoods / np.nanmax(Likelihoods)
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, MCSize)[0]
+
+ # Reject the poorly performed prior
+ accepted = normLikelihood >= unif
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(Likelihoods))
+ print(f'\nThe Naive MC-Estimation of BME is {logBME:.5f}.')
+
+ # Posterior-based expectation of likelihoods
+ postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
+
+ # Calculate Kullback-Leibler Divergence
+ KLD = postExpLikelihoods - logBME
+ print("The Kullback-Leibler divergence estimation is {KLD:.5f}.")
+
+ # -------------------------------------------------------------------------
+ # ----------------- Save the arrays as .npy files -------------------------
+ # -------------------------------------------------------------------------
+ if MCSize > 500000:
+ np.save(f"data/refBME_KLD_{ndim}.npy", (logBME, KLD))
+ np.save(f"data/mean_{ndim}.npy", np.mean(Outputs['Z'], axis=0))
+ np.save(f"data/std_{ndim}.npy", np.std(Outputs['Z'], axis=0))
+ else:
+ np.save(f"data/Prior_{ndim}.npy", xx)
+ np.save(f"data/origModelOutput_{ndim}.npy", Outputs[1:])
+ np.save(f"data/validLikelihoods_{ndim}.npy", Likelihoods)
diff --git a/examples/analytical-function_sequentialdesign/data/InputParameters_10.npy b/examples/analytical-function_sequentialdesign/data/InputParameters_10.npy
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diff --git a/examples/analytical-function_sequentialdesign/data/posterior/posterior_plot.py b/examples/analytical-function_sequentialdesign/data/posterior/posterior_plot.py
new file mode 100644
index 0000000000000000000000000000000000000000..840d0bcd7717f903750e6cadf8978e5d7df6b06a
--- /dev/null
+++ b/examples/analytical-function_sequentialdesign/data/posterior/posterior_plot.py
@@ -0,0 +1,52 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May 19 14:31:50 2022
+
+@author: farid
+"""
+import matplotlib.pyplot as plt
+import os
+import pandas as pd
+import seaborn as sns
+import numpy as np
+# Load the mplstyle
+plt.style.use(os.path.join(
+ os.path.split(__file__)[0],
+ '../../../../src/bayesvalidrox/', 'bayesvalidrox.mplstyle'))
+
+font_size = 80
+
+posterior_df = pd.read_csv('posterior_orig.csv')
+par_names = list(posterior_df.keys())
+n_params = len(par_names)
+posterior = posterior_df.values
+bound_tuples = [(-5, 5), (-5, 5)]
+
+folder = 'BAL_DKL'
+file = 'SeqPosterior_45'
+posterior = np.load(f'{folder}/{file}.npy')
+
+figPosterior, ax = plt.subplots(figsize=(15, 15))
+
+sns.kdeplot(x=posterior[:, 0], y=posterior[:, 1],
+ fill=True, ax=ax, cmap=plt.cm.jet,
+ clip=bound_tuples)
+# Axis labels
+plt.xlabel(par_names[0], fontsize=font_size)
+plt.ylabel(par_names[1], fontsize=font_size)
+
+# Set axis limit
+plt.xlim(bound_tuples[0])
+plt.ylim(bound_tuples[1])
+
+# Increase font size
+plt.xticks(fontsize=font_size)
+plt.yticks(fontsize=font_size)
+
+# Switch off the grids
+plt.grid(False)
+plt.show()
+# figPosterior.savefig("orig_posterior.pdf", bbox_inches='tight')
+figPosterior.savefig(f"seq_posterior_45_{folder}.pdf", bbox_inches='tight')
+plt.close()
diff --git a/examples/analytical-function_sequentialdesign/data/refBME_KLD_10.npy b/examples/analytical-function_sequentialdesign/data/refBME_KLD_10.npy
new file mode 100644
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diff --git a/examples/analytical-function_sequentialdesign/data/refBME_KLD_2.npy b/examples/analytical-function_sequentialdesign/data/refBME_KLD_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f6874ab10d08f3864e755b65d7cff94b0cabf81f
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diff --git a/examples/analytical-function_sequentialdesign/data/std_10.npy b/examples/analytical-function_sequentialdesign/data/std_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0ca99dbb88c8a6676a3cdf5a280bf34edc9685ed
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diff --git a/examples/analytical-function_sequentialdesign/data/std_2.npy b/examples/analytical-function_sequentialdesign/data/std_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..144f3abe232c4215984befeadc898d3f6601f6d8
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diff --git a/examples/analytical-function_sequentialdesign/data/validLikelihoods_10.npy b/examples/analytical-function_sequentialdesign/data/validLikelihoods_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e4646b7e7e1b0d33e1810488af485d5bb0679605
Binary files /dev/null and b/examples/analytical-function_sequentialdesign/data/validLikelihoods_10.npy differ
diff --git a/examples/analytical-function_sequentialdesign/data/validLikelihoods_2.npy b/examples/analytical-function_sequentialdesign/data/validLikelihoods_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..70971b581122eb48aca6fcf4961bdd39fd66b17a
Binary files /dev/null and b/examples/analytical-function_sequentialdesign/data/validLikelihoods_2.npy differ
diff --git a/examples/analytical-function_sequentialdesign/example_analytical_function.ipynb b/examples/analytical-function_sequentialdesign/example_analytical_function.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..e63948ddc4e636a1e0eef9834c706a40f5be6890
--- /dev/null
+++ b/examples/analytical-function_sequentialdesign/example_analytical_function.ipynb
@@ -0,0 +1,926 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "13c8e941",
+ "metadata": {},
+ "source": [
+ "# Example: Surrogate Model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "de58892b",
+ "metadata": {},
+ "source": [
+ "In this example, we train a surrogate model via the `bayesvalidrox` package. We aim at training a Polynomial Chaos Expansion to a simple analytical function. \n",
+ "The PCE representation of the computational model $M$ provides the dependence of this model on the uncertain model's parameters $\\mathbf{\\theta}$ using projection onto an orthonormal polynomial basis. It could be also seen as a linear regression that includes linear combinations of a fixed set of nonlinear functions with respect to the input variables, known as polynomial basis function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2890d7ef",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:PCE_Trunc}\n",
+ " M(x,y,z,t, \\mathbf{\\theta}) \\approx \\sum_{\\mathbf{\\alpha} \\in \\mathcal{A} } c_{\\mathbf{\\alpha}} (x,y,z,t) \\Psi_{\\mathbf{\\alpha}}(\\mathbf{\\theta}) \\, .\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bccdaebc",
+ "metadata": {},
+ "source": [
+ "Here, $x,y,z,t$ are the spatial and temporal components of the quantity of interest, $\\mathbf{\\theta}$ is the vector of the $N$ uncertain parameters of model $M$, $c_{\\mathbf{\\alpha}}(x,y,z,t) \\in \\mathbb{R}$ are the corresponding expansion coefficients that are functions of space and time, and $\\Psi_{\\mathbf{\\alpha}}(\\mathbf{\\theta})$ represents multivariate polynomials orthogonal with respect to a multi-index $\\mathbf{\\alpha}$. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "50023bea",
+ "metadata": {},
+ "source": [
+ "The latter represents the combinatoric information how to enumerate all possible products of $N$ individual univariate basis functions with respect to the total degree of expansions less or equal to polynomial degree $d$:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "538c43c8",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:truncation}\n",
+ "\\begin{split}\n",
+ " \\mathcal{A}^{N, d} = \\{ \\alpha \\in \\mathbb{N}^{N} \\ : \\ |\\alpha|\\leq d\\} \\, , \\qquad\n",
+ " \\text{card} \\ \\mathcal{A}^{N, d} \\equiv P = \\binom{N+d}{d}.\n",
+ "\\end{split}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b22c0ccb",
+ "metadata": {},
+ "source": [
+ "The multivariate polynomials $\\Psi_{\\alpha}(\\mathbf{\\theta})$ are comprised of the tensor product of univariate polynomials"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "41eeb9d3",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:Psi}\n",
+ " \\Psi_{\\alpha}(\\mathbf{\\theta}_k) := \\prod_{i=1}^{N_k} \\psi_{\\alpha_i}^{(i)}(\\mathbf{\\theta}_{k,i}) \\, ,\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "860cbcbd",
+ "metadata": {},
+ "source": [
+ "where the univariate orthonormal polynomials $\\psi_{\\alpha_i}^{(i)}(\\mathbf{\\theta}_{i})$ must satisfy "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "459de9cc",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:univPsi}\n",
+ " \\langle \\psi_j^{(i)}(\\mathbf{\\theta}_{k,i}), \\psi_l^{(i)}(\\mathbf{\\theta}_{k,i}) \\rangle := \\int_{\\Theta_{k,i}} \\psi_j^{(i)}(\\mathbf{\\theta}_{k,i}) \\psi_l^{(i)}(\\mathbf{\\theta}_{k,i}) f_{\\Theta_{k,i}} (\\mathbf{\\theta}_{k,i})d \\mathbf{\\theta}_{k,i} = \\delta_{j l} \\, .\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "34403fc6",
+ "metadata": {},
+ "source": [
+ "Here, $i$ represents the input variable with respect to which the polynomials are orthogonal as well as the corresponding polynomial family, $j$ and $l$ are the corresponding polynomial degree, $f_{\\Theta_{i}}(\\mathbf{\\theta}_{i})$ is the $i$th-input marginal distribution and $\\delta_{j l}$ is the Kronecker delta.\n",
+ "We use an arbitrary polynomial chaos expansion (aPCE), introduced by [Oladyshkin & Nowak (2012)](https://www.sciencedirect.com/science/article/pii/S0951832012000853?casa_token=pbisUgY4niQAAAAA:8WsqMi1mCyfUIJ3GnFGdv6FXFA6a4g8MB75kjGGdEvocV64cd4E8LxcSh8_fwZTeI2ONlUalq_8), that can operate with probability measures that may be implicitly and incompletely defined via their statistical moments. Using aPCE, one can build the multivariate orthonormal polynomials even in the absence of the exact probability density function $f_{\\Theta}(\\theta)$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3bd3feba",
+ "metadata": {},
+ "source": [
+ "In this tutorial, we use an extension of aPCE as Bayesian sparse arbitrary polynomial chaos (BsaPCE) representation. This method computes the coefficients $c_\\alpha$ in a Bayesian setting via a so-called Bayesian sparse learning approach, introduced by [Tipping (2001)](https://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf?ref=https://githubhelp.com)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6a291027",
+ "metadata": {},
+ "source": [
+ "The posterior distribution of the expansion coefficients, conditioned on the model responses $\\mathrm{\\mathbf{Y}}$ resulting from the training sets $\\mathbf{X}$, is given by the combination of a Gaussian likelihood and a Gaussian prior distribution over the unknown expansion coefficients $\\mathbf{c}$ according to Bayes' rule. Then, the posterior of the expansion coefficients given the model responses $\\mathrm{\\mathbf{Y}}$ and values of hyper-parameters $\\mathbf{\\alpha}$ and $\\beta$ describing the Gauss process, can take the following form"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3127c49a",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:PCE_Posterior}\n",
+ " p(\\mathrm{\\mathbf{c}}|\\mathbf{Y},\\mathbf{\\alpha}, \\beta) = \\frac{p(\\mathrm{\\mathbf{Y}}|\\mathbf{X},\\mathbf{c}, \\beta) p(\\mathbf{c}|\\mathbf{\\alpha})}{p(\\mathrm{\\mathbf{Y}}| \\mathbf{X}, \\mathbf{\\alpha} , \\beta)},\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "46381c6d",
+ "metadata": {},
+ "source": [
+ "which is also Gaussian defined by $\\mathcal{N}( \\mathbf{c}| \\mathbf{\\mu}, \\mathbf{\\Sigma})$ with"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "515d47e6",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:PCE_Posterior_moments}\n",
+ " \\mathbf{\\mu} = \\beta \\mathbf{\\Sigma} \\mathbf{\\Psi}^{\\top} \\mathrm{\\mathbf{Y}} \\, , \\qquad\n",
+ " \\mathbf{\\Sigma} = \\left(\\mathbf{A}+ \\mathbf{\\Psi}^{\\top} \\beta \\mathbf{\\Psi} \\right)^{-1} \\, .\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ce4636d9",
+ "metadata": {},
+ "source": [
+ "Here, $\\mathbf{\\Psi}$ is the design matrix of size $E \\times N$ with elements $\\Psi_{ni}=\\psi_i(x_n)$, where $E$ represents the number of model evaluations using the training samples, and $\\mathbf{A}=\\mathrm{diag}(\\alpha_i)$. The values of $\\mathbf{\\alpha}$ and $\\beta$ can be determined via type-II maximum likelihood [Berger (2013)](https://books.google.com/books?hl=en&lr=&id=1CDaBwAAQBAJ&oi=fnd&pg=PA1&dq=Statistical+decision+theory+and+Bayesian+analysis.++berger+2013&ots=LMulrdTL3O&sig=xMTVRCVf5scWBLQi98BgUie5d-M)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c50a317d",
+ "metadata": {},
+ "source": [
+ "## Problem description: Analytical function"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d13b9da3",
+ "metadata": {},
+ "source": [
+ "This test shows a surrogate-assisted Bayesian calibration of a time dependent non-linear analytical function of ten ($n=10$) uncertain parameters $\\omega=\\{\\omega_1, ..., \\omega_n\\}$, which reads as:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b715ea87",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\mathbf{y}(\\boldsymbol{\\omega}, t)=\\left(\\omega_{1}^{2}+\\omega_{2}-1\\right)^{2}+\\omega_{1}^{2}+0.1 \\omega_{1} \\exp \\left(\\omega_{2}\\right)-2 \\omega_{1} \\sqrt{0.5 t}+1+\\sum_{i=2}^{n} \\frac{\\omega_{i}^{3}}{i}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6625cdf6",
+ "metadata": {},
+ "source": [
+ "where the prior parameter distribution $p(\\omega)$ is considered to be independent and uniform with $\\omega_i \\sim \\mathcal{U} (-5, 5)$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "efe8f59c",
+ "metadata": {},
+ "source": [
+ "## Import necessary libraries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "31b60d45",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import sys\n",
+ "import joblib\n",
+ "from IPython.display import IFrame"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6d44d5af",
+ "metadata": {},
+ "source": [
+ "## Define the model with PyLinkForwardModel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bf3f4dfe",
+ "metadata": {},
+ "source": [
+ "We use the`PyLinkForwardModel`object for this purpose. Fistly, we are going to import the `bayesvalidrox` package and then, we instantiate the `PyLinkForwardModel` object."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "25a3b65a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from bayesvalidrox import PyLinkForwardModel\n",
+ "Model = PyLinkForwardModel()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "0452955f",
+ "metadata": {},
+ "source": [
+ "Next, we will pass the `link_type`, `name` and `py_file` variables to the `Model` object. Since the analytical function is implmented as a python function in a separate file, we only need to pass it's name (without `.py` extension) to the object variable `py_file`. Note that the function name in the python script should match that of the script. For models implemented as a separate python file, the `link_type` is `Function` to be given as a string. The `name` variable takes any user defined string."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "f26dbacd",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Model.link_type = 'Function'\n",
+ "Model.py_file = 'analytical_function'\n",
+ "Model.name = 'AnalyticFunc'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e12ef2ab",
+ "metadata": {},
+ "source": [
+ "The model output name is defined as follows:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "c2778a83",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Model.Output.names = ['Z'] # As a list of strings"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d4106fb6",
+ "metadata": {},
+ "source": [
+ "**Bonus**: For this example, we have a Monte-Carlo reference solution for the first moements (mean and standard deviation) of the analytical function. The numpy (`*.npy`) files can be found in the `data\\` directory. We will discuss the first two moments with our estimate moments using the surrogate model. These values can be passed in a form of a dictionary to the object variable `mc_reference`."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "9dc9e177",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "Model.mc_reference = {}\n",
+ "Model.mc_reference['Time [s]'] = np.arange(0, 10, 1.) / 9\n",
+ "Model.mc_reference['mean'] = np.load(f\"data/mean_2.npy\")\n",
+ "Model.mc_reference['std'] = np.load(f\"data/std_2.npy\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c2c68eee",
+ "metadata": {},
+ "source": [
+ "## Define probablistic input model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "af7f7d8f",
+ "metadata": {},
+ "source": [
+ "Now, we define the distribution of the model inputs. `bayesvalidrox` accepts the definition in two ways: by defining the distribution directly or by passing available data. The latter is handy, when little information is available on the parameters or they do not follow any typical distributions. We will use the second option and read the input parameters form a numpy file in the `data/` directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "f1d2deb0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Import and instantiate the input object\n",
+ "from bayesvalidrox import Input\n",
+ "Inputs = Input()\n",
+ "\n",
+ "# Option I: Define distribution directy with their name, type and parameters \n",
+ "\n",
+ "# First parameter\n",
+ "Inputs.add_marginals()\n",
+ "Inputs.Marginals[0].name = '$X_1$'\n",
+ "Inputs.Marginals[0].dist_type = 'unif'\n",
+ "Inputs.Marginals[0].parameters = [-5, 5]\n",
+ "\n",
+ "# Second parameter\n",
+ "Inputs.add_marginals()\n",
+ "Inputs.Marginals[1].name = '$X_2$'\n",
+ "Inputs.Marginals[1].dist_type = 'unif'\n",
+ "Inputs.Marginals[1].parameters = [-5, 5]\n",
+ "\n",
+ "# ----------------------------------------------------------------------------\n",
+ "\n",
+ "# Option II: Pass available data for input parameters\n",
+ "# inputParams = np.load('data/InputParameters_2.npy')\n",
+ "\n",
+ "# First parameter\n",
+ "# Inputs.add_marginals()\n",
+ "# Inputs.Marginals[0].name = '$X_1$'\n",
+ "# Inputs.Marginals[0].input_data = inputParams[:, 0]\n",
+ "\n",
+ "# Second parameter\n",
+ "# Inputs.add_marginals()\n",
+ "# Inputs.Marginals[1].name = '$X_2$'\n",
+ "# Inputs.Marginals[1].input_data = inputParams[:, 1]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "10ff4b23",
+ "metadata": {},
+ "source": [
+ "## Define surrogate (meta) model"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d0e8a911",
+ "metadata": {},
+ "source": [
+ "In this example, we use a Polynomial Chaos Expansion (PCE) as our meta model. Like before, we need to import the `MetaModel` object from `bayesvalidrox` package and instantiate a meta-model object. This object, however, accepts the input object (`Input`) as an argument."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "7256d8f0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from bayesvalidrox import MetaModel\n",
+ "MetaModelOpts = MetaModel(Inputs)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aa7756f5",
+ "metadata": {},
+ "source": [
+ "Let us define now the meta model type, the regression type, degree of the polynomials and the trunction norm `q_norm` which lies between 0 and 1. This parameter defines hyperbolic truncation scheme. As for `meta_model_type`, there are two PCE implementations available in `bayesvalidrox`, namely generalized PCE (`PCE`) [Xiu & Karniadakis (2002)](https://doi.org/10.1137/S1064827501387826) or its arbitrary extension (`aPCE`) [Oladyshkin & Nowak (2012)](https://doi.org/10.1016/j.ress.2012.05.002)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "39a2ece3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Select your metamodel method\n",
+ "# Options: PCE and aPCE\n",
+ "MetaModelOpts.meta_model_type = 'aPCE'\n",
+ "\n",
+ "# Select the regression method for calculation of the PCE coefficients:\n",
+ "# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression\n",
+ "# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression\n",
+ "# 5)FastARD: Fast Bayesian ARD Regression\n",
+ "# 6)VBL: Variational Bayesian Learning\n",
+ "# 7)EBL: Emperical Bayesian Learning\n",
+ "MetaModelOpts.pce_reg_method = 'FastARD'\n",
+ "\n",
+ "\n",
+ "# Specify the polynomial degree to be compared by the adaptive algorithm:\n",
+ "# The degree with the lowest Leave-One-Out cross-validation (LOO)\n",
+ "# error (or the highest score=1-LOO)estimator is chosen as the final\n",
+ "# metamodel. pce_deg accepts degree as a scalar or a range.\n",
+ "MetaModelOpts.pce_deg = np.arange(9)\n",
+ "\n",
+ "# Hyperbolic truncation scheme 0<q<1 (default=1)\n",
+ "MetaModelOpts.pce_q_norm = 0.75"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a3048f38",
+ "metadata": {},
+ "source": [
+ "After defining the metamodel type, we need to define the so-called experimental design (ExpDesign). ExpDesign basically provides instruction on how to samplie the input parameter space."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "f8e1bf2d",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ------------------------------------------------\n",
+ "# ------ Experimental Design Configuration -------\n",
+ "# ------------------------------------------------\n",
+ "MetaModelOpts.add_ExpDesign()\n",
+ "\n",
+ "# One-shot (normal) or Sequential Adaptive (sequential) Design\n",
+ "MetaModelOpts.ExpDesign.Method = 'normal'\n",
+ "MetaModelOpts.ExpDesign.n_init_samples = 100\n",
+ "\n",
+ "# Sampling methods\n",
+ "# 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov\n",
+ "# 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user\n",
+ "MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8f7cd8dc",
+ "metadata": {},
+ "source": [
+ "Now, we can start training the surrogate (meta-) model by using the `create_metamodel` method and passing the model object as the only argument."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "82fffca5",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Computing orth. polynomial coeffs: 100%|##########| 2/2 [00:02<00:00, 1.42s/it]"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Now the forward model needs to be run!\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Running forward model : 100%|██████████| 100/100 [00:00<00:00, 6414.49it/s]\n",
+ "Fitting regression: 0%| | 0/1 [00:00<?, ?it/s]"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ ">>>> Training the aPCE metamodel started. <<<<<<\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Fitting regression: 100%|██████████| 1/1 [00:04<00:00, 4.51s/it]"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ ">>>> Training the aPCE metamodel sucessfully completed. <<<<<<\n",
+ "\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Train the meta model\n",
+ "PCEModel = MetaModelOpts.create_metamodel(Model)\n",
+ "\n",
+ "# Save PCE models as pkl object for further deployment for example on a cloud\n",
+ "with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:\n",
+ " joblib.dump(PCEModel, output, 2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "4b2b6a1b",
+ "metadata": {},
+ "source": [
+ "## Post-processing"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "64ea5912",
+ "metadata": {},
+ "source": [
+ "As before, we need to import the `PostProcessing` module of `bayesvalidrox` and instantiate it. Bear in mind that it accepts the meta-model object `PCEModel` as the only argument."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "d51e4195",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from bayesvalidrox import PostProcessing\n",
+ "PostPCE = PostProcessing(PCEModel)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "51aed43d",
+ "metadata": {},
+ "source": [
+ "### Moment comparison"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "69de7856",
+ "metadata": {},
+ "source": [
+ "Since the reference moments obtained from a Monte-Carlo simulation is available, we only need to call the `plotMoments` method from the PostProcessing object. This method generates a plot and stores it in `Outputs_PostProcessing_calib` directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "96e85fb9",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " Time [s] mean std\n",
+ "0 0.000000 126.943408 170.920339\n",
+ "1 0.111111 126.941468 170.889593\n",
+ "2 0.222222 126.940664 170.880029\n",
+ "3 0.333333 126.940047 170.873950\n",
+ "4 0.444444 126.939527 170.869675\n",
+ "5 0.555556 126.939069 170.866553\n",
+ "6 0.666667 126.938655 170.864251\n",
+ "7 0.777778 126.938274 170.862569\n",
+ "8 0.888889 126.937919 170.861378\n",
+ "9 1.000000 126.937586 170.860589\n",
+ "\n",
+ ">>>>> Moments of Z <<<<<\n",
+ "\n",
+ "Index | Mean | Std. deviation\n",
+ "-----------------------------------\n",
+ "1 | 1.266e+02 | 1.705e+02\n",
+ "2 | 1.266e+02 | 1.705e+02\n",
+ "3 | 1.266e+02 | 1.705e+02\n",
+ "4 | 1.266e+02 | 1.705e+02\n",
+ "5 | 1.266e+02 | 1.705e+02\n",
+ "6 | 1.266e+02 | 1.705e+02\n",
+ "7 | 1.266e+02 | 1.705e+02\n",
+ "8 | 1.266e+02 | 1.705e+02\n",
+ "9 | 1.266e+02 | 1.705e+02\n",
+ "10 | 1.266e+02 | 1.705e+02\n",
+ "----------------------------------------\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"900\"\n",
+ " height=\"600\"\n",
+ " src=\"./Outputs_PostProcessing_calib/Mean_Std_PCE.pdf\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x7f44a48ed670>"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<Figure size 1728x1152 with 0 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Compute the moments and compare with the Monte-Carlo reference\n",
+ "PostPCE.plot_moments()\n",
+ "# Show the pdf\n",
+ "IFrame(\"./Outputs_PostProcessing_calib/Mean_Std_PCE.pdf\", width=900, height=600)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a6cf5333",
+ "metadata": {},
+ "source": [
+ "### Validation of the metamodel"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9d506ae2",
+ "metadata": {},
+ "source": [
+ "Let us first visually compare the results of the metamodel and the original model, i.e. `Analyrical Function` for 3 randomly drawn samples for the prior parameter distribution. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "cfd42c02",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Running forward model valid: 100%|██████████| 3/3 [00:00<00:00, 3583.85it/s]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"900\"\n",
+ " height=\"600\"\n",
+ " src=\"./Outputs_PostProcessing_calib/Model_vs_PCEModel.pdf\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x7f44a47a7bb0>"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<Figure size 1728x1152 with 0 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot to check validation visually.\n",
+ "PostPCE.valid_metamodel(n_samples=3)\n",
+ "# Show the pdf\n",
+ "IFrame(\"./Outputs_PostProcessing_calib/Model_vs_PCEModel.pdf\", width=900, height=600)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3b39e05f",
+ "metadata": {},
+ "source": [
+ "Another way to check the accuracy of the meta model is to use the `accuracyCheckMetaModel` method to show the Root Mean Square Error and the validation error. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "e2f83de2",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Running forward model validSet: 100%|██████████| 200/200 [00:00<00:00, 8584.59it/s]"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ ">>>>> Errors of Z <<<<<\n",
+ "\n",
+ "Index | RMSE | Validation Error\n",
+ "-----------------------------------\n",
+ "1 | 4.415e-01 | 3.393e-08\n",
+ "2 | 4.415e-01 | 3.399e-08\n",
+ "3 | 4.415e-01 | 3.402e-08\n",
+ "4 | 4.415e-01 | 3.404e-08\n",
+ "5 | 4.415e-01 | 3.406e-08\n",
+ "6 | 4.416e-01 | 3.408e-08\n",
+ "7 | 4.418e-01 | 3.412e-08\n",
+ "8 | 4.458e-01 | 3.475e-08\n",
+ "9 | 4.410e-01 | 3.401e-08\n",
+ "10 | 4.412e-01 | 3.405e-08\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Compute and print RMSE error\n",
+ "PostPCE.accuracyCheckMetaModel(nSamples=200)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ef686ae7",
+ "metadata": {},
+ "source": [
+ "### Global sensitivity analysis with Sobol indices"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1ffecd15",
+ "metadata": {},
+ "source": [
+ "Here, we analyze how the variability of the model response quantity (`Z`) is affected by the variability of each input variable or combinations thereof. Here, we use the so-called Sobol indices ([Sobol original paper](https://mae.ufl.edu/haftka/eoed/protected/Sobol%20Original%20Paper.pdf)), derived from a variance decomposition of model outputs in terms of contributions of each input parameter or combinations thereof. \n",
+ "Using Sobol decomposition, one can describe the total variance of the model in terms of the sum of the summands' variances. Once the PC representation of the model is available, the expansion coefficients are simply gathered according to the dependency of each basis polynomial, square-summed and normalized"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3e95b594",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:pce-sobol-1st}\n",
+ "\\begin{array}{l}\n",
+ "S_{i_{1}, \\ldots, i_{s}}=\\frac{\\sum\\limits_{j=1}^{M} \\chi_{j} c_{j}^{2}}{\\sum\\limits_{j=1}^{M} c_{j}^{2}} \\, ,\\qquad\n",
+ "\\chi_{j}=\\left\\{\\begin{array}{ll}\n",
+ "1, & \\text { if } \\alpha_{j}^{k}>0, \\quad \\forall j \\in\\left(i_{1}, \\ldots, i_{s}\\right) \\\\[0.5em]\n",
+ "0, & \\text { if } \\alpha_{j}^{k}=0, \\quad \\exists j \\in\\left(i_{1}, \\ldots, i_{s}\\right)\n",
+ "\\end{array}\\right\\} \\, .\n",
+ "\\end{array}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a255fc43",
+ "metadata": {},
+ "source": [
+ "Here, $S_{i_{1}, \\ldots, i_{s}}$ is the Sobol index that indicates what fraction of total variance of the response quantity can be traced back to the joint contributions of the parameters $\\theta_{i_{1}}, \\ldots, \\theta_{i_{s}}.$ The index selection operator $\\chi_{j}$ indicates where the chosen parameters $\\theta$ numbered as $i_{1}, \\ldots, i_{s}$ (i.e., $\\left.\\theta_{i_{1}}, \\ldots, \\theta_{i_{s}}\\right)$ have concurrent contributions to the variance within the overall expansion. Simply put, it selects all polynomial terms with the specified combination $i_{1}, \\ldots, i_{s}$ of model parameters."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "025e4a83",
+ "metadata": {},
+ "source": [
+ "A complementing measure for sensitivity analysis is the Sobol Total Index. It expresses the total contribution to the variance of model output due to the uncertainty of an individual parameter $\\theta_j$ in all cross-combinations with other parameters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9da5d910",
+ "metadata": {},
+ "source": [
+ "\\begin{equation}\n",
+ "\\label{eq:pce-sobol-total}\n",
+ "S_{j}^{T}=\\sum_{\\left\\{i_{1}, \\ldots, i_{s}\\right\\} \\supset j} S_{i_{1}, \\ldots, i_{s}},\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "59413b8c",
+ "metadata": {},
+ "source": [
+ "where $S_{j}^{T}$ is simply a summation of all Sobol indices in which the variable $\\theta_j$ appears as univariate as well as joint influences.\n",
+ "The Total Sobol indices sum to one, if input variables are independent. When dealing with correlated variables, however, this is not the case."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "962bf769",
+ "metadata": {},
+ "source": [
+ "To perform the sensitivity analysis with `bayesvalidrox` package, we need to call the `sobolIndicesPCE` of the `PostProcessing` object. This returns two dictionaries containing the single sobol indices and the total ones. Moreover, it plots the Total Sobol Indices and stores the plots in `pdf` format in `Outputs_PostProcessing_calib` directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "135173d6",
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ " <iframe\n",
+ " width=\"900\"\n",
+ " height=\"600\"\n",
+ " src=\"./Outputs_PostProcessing_calib/Sobol_indices.pdf\"\n",
+ " frameborder=\"0\"\n",
+ " allowfullscreen\n",
+ " ></iframe>\n",
+ " "
+ ],
+ "text/plain": [
+ "<IPython.lib.display.IFrame at 0x7fe0b57d1340>"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<Figure size 1728x1152 with 0 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the sobol indices\n",
+ "sobol_cell, total_sobol = PostPCE.sobolIndicesPCE()\n",
+ "# Show the pdf\n",
+ "IFrame(\"./Outputs_PostProcessing_calib/Sobol_indices.pdf\", width=900, height=600)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/examples/analytical-function_sequentialdesign/example_analytical_function.py b/examples/analytical-function_sequentialdesign/example_analytical_function.py
new file mode 100644
index 0000000000000000000000000000000000000000..09261acba65231d3b9782d06fa10ce8c18a95085
--- /dev/null
+++ b/examples/analytical-function_sequentialdesign/example_analytical_function.py
@@ -0,0 +1,337 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test shows a surrogate-assisted Bayesian calibration of a time dependent
+ analytical function.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Aug 9 2019
+
+"""
+
+import numpy as np
+import pandas as pd
+import sys
+import joblib
+import matplotlib
+matplotlib.use('agg')
+
+# import bayesvalidrox
+# Add BayesValidRox path
+sys.path.append("src/")
+sys.path.append("../../src/")
+
+import bayesvalidrox
+from bayesvalidrox import PyLinkForwardModel
+
+from bayesvalidrox.pylink.pylink import PyLinkForwardModel
+from bayesvalidrox.surrogate_models.inputs import Input
+from bayesvalidrox.surrogate_models.exp_designs import ExpDesigns
+from bayesvalidrox.surrogate_models.surrogate_models import MetaModel
+#from bayesvalidrox.surrogate_models.meta_model_engine import MetaModelEngine
+from bayesvalidrox.post_processing.post_processing import PostProcessing
+from bayesvalidrox.bayes_inference.bayes_inference import BayesInference
+from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
+
+from bayesvalidrox.surrogate_models.engine import Engine
+
+if __name__ == "__main__":
+
+ # Number of parameters
+ ndim = 10 # 2, 10
+
+ # =====================================================
+ # ============= COMPUTATIONAL MODEL ================
+ # =====================================================
+ Model = PyLinkForwardModel()
+
+ Model.link_type = 'Function'
+ Model.py_file = 'analytical_function'
+ Model.name = 'AnalyticFunc'
+
+ Model.Output.names = ['Z']
+
+ # For Bayesian inversion synthetic data with X=[0,0]
+ Model.observations = {}
+ Model.observations['Time [s]'] = np.arange(0, 10, 1.) / 9
+ Model.observations['Z'] = np.repeat([2.], 10)
+
+ # For Checking with the MonteCarlo refrence
+ Model.mc_reference = {}
+ Model.mc_reference['Time [s]'] = np.arange(0, 10, 1.) / 9
+ Model.mc_reference['mean'] = np.load(f"data/mean_{ndim}.npy")
+ Model.mc_reference['std'] = np.load(f"data/std_{ndim}.npy")
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ # Define the uncertain parameters with their mean and
+ # standard deviation
+ Inputs = Input()
+
+ # Assuming dependent input variables
+ # Inputs.Rosenblatt = True
+
+ for i in range(ndim):
+ Inputs.add_marginals()
+ Inputs.Marginals[i].name = "$\\theta_{"+str(i+1)+"}$"
+ Inputs.Marginals[i].dist_type = 'uniform'
+ Inputs.Marginals[i].parameters = [-5, 5]
+
+ # arbitrary polynomial chaos
+ # inputParams = np.load('data/InputParameters_{}.npy'.format(ndim))
+ # for i in range(ndim):
+ # Inputs.add_marginals()
+ # Inputs.Marginals[i].name = f'$X_{i+1}$'
+ # Inputs.Marginals[i].input_data = inputParams[:, i]
+
+ # =====================================================
+ # ========== DEFINITION OF THE METAMODEL ============
+ # =====================================================
+ MetaModelOpts = MetaModel(Inputs)#, Model)
+
+ # Select if you want to preserve the spatial/temporal depencencies
+ # MetaModelOpts.dim_red_method = 'PCA'
+ # MetaModelOpts.var_pca_threshold = 99.999
+ # MetaModelOpts.n_pca_components = 10
+
+ # Select your metamodel method
+ # 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
+ # 3) GPE (Gaussian Process Emulator)
+ MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'FastARD'
+
+ # Bootstraping
+ # 1) normal 2) fast
+ MetaModelOpts.bootstrap_method = 'fast'
+ MetaModelOpts.n_bootstrap_itrs = 1
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ MetaModelOpts.pce_deg = 12
+
+ # q-quasi-norm 0<q<1 (default=1)
+ MetaModelOpts.pce_q_norm = 0.85 if ndim < 5 else 0.5
+
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
+ # ------------------------------------------------
+ # ------ Experimental Design Configuration -------
+ # ------------------------------------------------
+ ExpDesign = ExpDesigns(Inputs)
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ ExpDesign.method = 'sequential'
+ ExpDesign.n_init_samples = 140#00#3*ndim
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley
+ # 6) chebyshev(FT) 7) grid(FT) 8)user
+ ExpDesign.sampling_method = 'latin_hypercube'
+
+ # Provide the experimental design object with a hdf5 file
+ #ExpDesign.hdf5_file = 'ExpDesign_AnalyticFunc.hdf5'
+
+ # Set the sampling parameters
+ ExpDesign.n_new_samples = 1
+ ExpDesign.n_max_samples = 141#150 # sum of init + sequential
+ ExpDesign.mod_LOO_threshold = 1e-16
+
+ # ExpDesign.adapt_verbose = True
+ # 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
+ ExpDesign.tradeoff_scheme = None
+ # MetaModelOpts.ExpDesign.n_replication = 5
+ # -------- Exploration ------
+ # 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'LOOCV' 5)'dual annealing'
+ ExpDesign.explore_method = 'random'
+
+ # Use when 'dual annealing' chosen
+ ExpDesign.max_func_itr = 1000
+
+ # Use when 'Voronoi' or 'random' or 'latin_hypercube' chosen
+ ExpDesign.n_canddidate = 1000
+ ExpDesign.n_cand_groups = 4
+
+ # -------- Exploitation ------
+ # 1)'BayesOptDesign' 2)'BayesActDesign' 3)'VarOptDesign' 4)'alphabetic'
+ # 5)'Space-filling'
+ ExpDesign.exploit_method = 'Space-filling'
+ ExpDesign.exploit_method = 'BayesActDesign'
+ ExpDesign.util_func = 'DKL'
+
+ # BayesOptDesign/BayesActDesign -> when data is available
+ # 1) MI (Mutual information) 2) ALC (Active learning McKay)
+ # 2)DKL (Kullback-Leibler Divergence) 3)DPP (D-Posterior-percision)
+ # 4)APP (A-Posterior-percision) # ['DKL', 'BME', 'infEntropy']
+ # MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # BayesActDesign -> when data is available
+ # 1) BME (Bayesian model evidence) 2) infEntropy (Information entropy)
+ # 2)DKL (Kullback-Leibler Divergence)
+ #MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # VarBasedOptDesign -> when data is not available
+ # 1)ALM 2)EIGF, 3)LOOCV
+ # or a combination as a list
+ # MetaModelOpts.ExpDesign.util_func = 'EIGF'
+
+ # alphabetic
+ # 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
+ # 3)K-Opt (K-Optimality) or a combination as a list
+ # MetaModelOpts.ExpDesign.util_func = 'D-Opt'
+
+ # Defining the measurement error, if it's known a priori
+ obsData = pd.DataFrame(Model.observations, columns=Model.Output.names)
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obsData**2
+ MetaModelOpts.Discrepancy = DiscrepancyOpts
+
+ # Plot the posterior snapshots for SeqDesign
+ ExpDesign.post_snapshot = False
+ ExpDesign.step_snapshot = 1
+ ExpDesign.max_a_post = [0] * ndim
+
+ # For calculation of validation error for SeqDesign
+ prior = np.load(f"data/Prior_{ndim}.npy")
+ prior_outputs = np.load(f"data/origModelOutput_{ndim}.npy")
+ likelihood = np.load(f"data/validLikelihoods_{ndim}.npy")
+ ExpDesign.valid_samples = prior[:500]
+ ExpDesign.valid_model_runs = {'Z': prior_outputs[:500]}
+
+
+ # Run using the new engine
+ #engine = Engine(MetaModelOpts, Model, ExpDesign)
+ #engine.start_engine()
+ #engine.train_normal()
+
+ MetaModelOpts.ExpDesign = ExpDesign
+ engine = Engine(MetaModelOpts, Model, ExpDesign)
+ engine.start_engine()
+ #engine.train_sequential()
+ engine.train_normal()
+
+ # Load the objects
+ # with open(f"PCEModel_{Model.name}.pkl", "rb") as input:
+ # PCEModel = joblib.load(input)
+
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ PostPCE = PostProcessing(engine)
+
+ # Plot to check validation visually.
+ PostPCE.valid_metamodel(n_samples=1)
+
+ # Compute and print RMSE error
+ PostPCE.check_accuracy(n_samples=300)
+
+ # Compute the moments and compare with the Monte-Carlo reference
+ if MetaModelOpts.meta_model_type != 'GPE':
+ PostPCE.plot_moments()
+
+ # Plot the evolution of the KLD,BME, and Modified LOOCV error
+ if MetaModelOpts.ExpDesign.method == 'sequential':
+ refBME_KLD = np.load("data/refBME_KLD_"+str(ndim)+".npy")
+ PostPCE.plot_seq_design_diagnostics(refBME_KLD)
+
+ # Plot the sobol indices
+ if MetaModelOpts.meta_model_type != 'GPE':
+ total_sobol = PostPCE.sobol_indices()
+
+ # =====================================================
+ # ======== Bayesian inference with Emulator ==========
+ # =====================================================
+ BayesOpts = BayesInference(engine)
+ BayesOpts.emulator = True
+ BayesOpts.plot_post_pred = True
+
+ # BayesOpts.selected_indices = [0, 3, 5, 7, 9]
+ # BME Bootstrap
+ BayesOpts.bootstrap = True
+ BayesOpts.n_bootstrap_itrs = 500
+ BayesOpts.bootstrap_noise = 100
+
+ # Bayesian cross validation
+ BayesOpts.bayes_loocv = True # TODO: test what this does
+
+ # Select the inference method
+ import emcee
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters passed to self.mcmc_params
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e4,#5,
+ 'n_walkers': 30,
+ 'moves': emcee.moves.KDEMove(),
+ 'multiprocessing': False,
+ 'verbose': False
+ }
+
+ # ----- Define the discrepancy model -------
+ obsData = pd.DataFrame(Model.observations, columns=Model.Output.names)
+ BayesOpts.measurement_error = obsData
+
+ # # -- (Option B) --
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obsData**2
+ BayesOpts.Discrepancy = DiscrepancyOpts
+
+ # -- (Option C) --
+ if 0:
+ DiscOutputOpts = Input()
+ # # # OutputName = 'Z'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[0].Nnme = '$\sigma^2_{\epsilon}$'
+ DiscOutputOpts.Marginals[0].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[0].parameters = [0, 10]
+ #BayesOpts.Discrepancy = {'known': DiscrepancyOpts,
+ # 'infer': Discrepancy(DiscOutputOpts)}
+
+ BayesOpts.bias_inputs = {'Z':np.arange(0, 10, 1.).reshape(-1,1) / 9}
+
+ DiscOutputOpts = Input()
+ # OutputName = 'lambda'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[0].name = '$\lambda$'
+ DiscOutputOpts.Marginals[0].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[0].parameters = [0, 1]
+
+ # # OutputName = 'sigma_f'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[1].Name = '$\sigma_f$'
+ DiscOutputOpts.Marginals[1].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[1].parameters = [0, 1e-4]
+ #BayesOpts.Discrepancy = Discrepancy(DiscOutputOpts)
+ BayesOpts.Discrepancy = {'known': DiscrepancyOpts,
+ 'infer': Discrepancy(DiscOutputOpts)}
+
+ # Start the calibration/inference
+ Bayes_PCE = BayesOpts.create_inference()
+
+ # Save class objects
+ with open(f'Bayes_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(Bayes_PCE, output, 2)
diff --git a/examples/analytical-function_sequentialdesign/example_analytical_function_testSequential.py b/examples/analytical-function_sequentialdesign/example_analytical_function_testSequential.py
new file mode 100644
index 0000000000000000000000000000000000000000..7739966ea11b73d4f0985a654478a75e874deca7
--- /dev/null
+++ b/examples/analytical-function_sequentialdesign/example_analytical_function_testSequential.py
@@ -0,0 +1,435 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test shows a surrogate-assisted Bayesian calibration of a time dependent
+ analytical function.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Aug 9 2019
+
+"""
+
+import numpy as np
+import pandas as pd
+import sys
+import joblib
+import matplotlib
+#matplotlib.use('agg')
+
+# import bayesvalidrox
+# Add BayesValidRox path
+sys.path.append("../../src/")
+
+from bayesvalidrox.surrogate_models.inputs import Input
+from bayesvalidrox.surrogate_models.input_space import InputSpace
+from bayesvalidrox.pylink.pylink import PyLinkForwardModel
+from bayesvalidrox.surrogate_models.inputs import Input
+from bayesvalidrox.surrogate_models.exp_designs import ExpDesigns
+from bayesvalidrox.surrogate_models.surrogate_models import MetaModel
+#from bayesvalidrox.surrogate_models.meta_model_engine import MetaModelEngine
+from bayesvalidrox.post_processing.post_processing import PostProcessing
+from bayesvalidrox.bayes_inference.bayes_inference import BayesInference
+from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
+
+from bayesvalidrox.surrogate_models.engine import Engine
+
+if __name__ == "__main__":
+
+ # Number of parameters
+ ndim = 2#10 # 2, 10
+
+ # =====================================================
+ # ============= COMPUTATIONAL MODEL ================
+ # =====================================================
+ Model = PyLinkForwardModel()
+
+ Model.link_type = 'Function'
+ Model.py_file = 'analytical_function'
+ Model.name = 'AnalyticFunc'
+
+ Model.Output.names = ['Z']
+
+ # For Bayesian inversion synthetic data with X=[0,0]
+ Model.observations = {}
+ Model.observations['Time [s]'] = np.arange(0, 10, 1.) / 9
+ Model.observations['Z'] = np.repeat([2.], 10)
+
+ # For Checking with the MonteCarlo refrence
+ Model.mc_reference = {}
+ Model.mc_reference['Time [s]'] = np.arange(0, 10, 1.) / 9
+ Model.mc_reference['mean'] = np.load(f"data/mean_{ndim}.npy")
+ Model.mc_reference['std'] = np.load(f"data/std_{ndim}.npy")
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ # Define the uncertain parameters with their mean and
+ # standard deviation
+ Inputs = Input()
+
+ # Assuming dependent input variables
+ # Inputs.Rosenblatt = True
+
+ for i in range(ndim):
+ Inputs.add_marginals()
+ Inputs.Marginals[i].name = "$\\theta_{"+str(i+1)+"}$"
+ Inputs.Marginals[i].dist_type = 'uniform'
+ Inputs.Marginals[i].parameters = [-5, 5]
+
+ # arbitrary polynomial chaos
+ # inputParams = np.load('data/InputParameters_{}.npy'.format(ndim))
+ # for i in range(ndim):
+ # Inputs.add_marginals()
+ # Inputs.Marginals[i].name = f'$X_{i+1}$'
+ # Inputs.Marginals[i].input_data = inputParams[:, i]
+
+ # =====================================================
+ # ========== DEFINITION OF THE METAMODEL ============
+ # =====================================================
+ MetaModelOpts = MetaModel(Inputs)#, Model)
+
+ # Select if you want to preserve the spatial/temporal depencencies
+ # MetaModelOpts.dim_red_method = 'PCA'
+ # MetaModelOpts.var_pca_threshold = 99.999
+ # MetaModelOpts.n_pca_components = 10
+
+ # Select your metamodel method
+ # 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
+ # 3) GPE (Gaussian Process Emulator)
+ MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'FastARD'
+
+ # Bootstraping
+ # 1) normal 2) fast
+ MetaModelOpts.bootstrap_method = 'fast'
+ MetaModelOpts.n_bootstrap_itrs = 1
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ MetaModelOpts.pce_deg = 12
+
+ # q-quasi-norm 0<q<1 (default=1)
+ MetaModelOpts.pce_q_norm = 0.85 if ndim < 5 else 0.5
+
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
+ # ------------------------------------------------
+ # ------ Experimental Design Configuration -------
+ # ------------------------------------------------
+ ExpDesign = ExpDesigns(Inputs)
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ ExpDesign.method = 'sequential'
+ ExpDesign.n_init_samples = 140#00#3*ndim
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley
+ # 6) chebyshev(FT) 7) grid(FT) 8)user
+ ExpDesign.sampling_method = 'latin_hypercube'
+
+ # Provide the experimental design object with a hdf5 file
+ #ExpDesign.hdf5_file = 'ExpDesign_AnalyticFunc.hdf5'
+
+ # Set the sampling parameters
+ ExpDesign.n_new_samples = 1
+ ExpDesign.n_max_samples = 141#150 # sum of init + sequential
+ ExpDesign.mod_LOO_threshold = 1e-16
+
+ # ExpDesign.adapt_verbose = True
+
+ # 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
+ ExpDesign.tradeoff_scheme = None
+
+ # MetaModelOpts.ExpDesign.n_replication = 5
+
+ # -------- Exploration ------
+ # 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'LOOCV' 5)'dual annealing'
+ ExpDesign.explore_method = 'random'
+
+ # Use when 'dual annealing' chosen
+ ExpDesign.max_func_itr = 1000
+
+ # Use when 'Voronoi' or 'random' or 'latin_hypercube' chosen
+ ExpDesign.n_canddidate = 1000
+ ExpDesign.n_cand_groups = 4
+
+ # -------- Exploitation ------
+ # 1)'BayesOptDesign' 2)'BayesActDesign' 3)'VarOptDesign' 4)'alphabetic'
+ # 5)'Space-filling'
+ ExpDesign.exploit_method = 'Space-filling'
+ ExpDesign.exploit_method = 'BayesActDesign'
+ ExpDesign.util_func = 'DKL'
+
+ # BayesOptDesign/BayesActDesign -> when data is available
+ # 1) MI (Mutual information) 2) ALC (Active learning McKay)
+ # 2)DKL (Kullback-Leibler Divergence) 3)DPP (D-Posterior-percision)
+ # 4)APP (A-Posterior-percision) # ['DKL', 'BME', 'infEntropy']
+ # MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # BayesActDesign -> when data is available
+ # 1) BME (Bayesian model evidence) 2) infEntropy (Information entropy)
+ # 2)DKL (Kullback-Leibler Divergence)
+ #MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # VarBasedOptDesign -> when data is not available
+ # 1)ALM 2)EIGF, 3)LOOCV
+ # or a combination as a list
+ # MetaModelOpts.ExpDesign.util_func = 'EIGF'
+
+ # alphabetic
+ # 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
+ # 3)K-Opt (K-Optimality) or a combination as a list
+ # MetaModelOpts.ExpDesign.util_func = 'D-Opt'
+
+ # Defining the measurement error, if it's known a priori
+ obsData = pd.DataFrame(Model.observations, columns=Model.Output.names)
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obsData**2
+ MetaModelOpts.Discrepancy = DiscrepancyOpts
+
+ # Plot the posterior snapshots for SeqDesign
+ ExpDesign.post_snapshot = False
+ ExpDesign.step_snapshot = 1
+ ExpDesign.max_a_post = [0] * ndim
+
+ # For calculation of validation error for SeqDesign
+ prior = np.load(f"data/Prior_{ndim}.npy")
+ prior_outputs = np.load(f"data/origModelOutput_{ndim}.npy")
+ likelihood = np.load(f"data/validLikelihoods_{ndim}.npy")
+ ExpDesign.valid_samples = prior[:500]
+ ExpDesign.valid_model_runs = {'Z': prior_outputs[:500]}
+
+ # Do the standard training of the surrogate and init of the engine
+ MetaModelOpts.ExpDesign = ExpDesign
+ engine = Engine(MetaModelOpts, Model, ExpDesign)
+ engine.start_engine()
+ engine.train_normal()
+
+#%% Test combinations of the sequential strategies
+ """
+ This part of the code tests the available combinations of the
+ sequential strategies.
+ The following combinations have remaining issues to be solved:
+ - exploration = 'Voronoi' creates mismatching numbers of candidates and weights
+ - exploration = 'loocv' needs MetaModel.create_ModelError, which does not exist
+ - exploration = 'dual annealing' restricted in what it allows as exploitation methods
+ - tradeoff = 'adaptive' perhaps not possible in the first AL iteration?
+
+ The following combinations are running through:
+ Tradeoff
+ - None
+ - equal
+ - epsilon-decreasing
+ Exploration
+ - random
+ - global_mc
+ Exploitation
+ - BayesActDesign
+ - VarOptDesign
+ - alphabetic
+ - space-filling
+
+ Performance notes:
+ - BayesOptDesign slow in the OptBayesianDesign iterations
+ - exploitation = 'BayesOptDesign' has circular dependency with the engine class
+
+ # TODO: user-defined options were left out in this test for both
+ sampling-methods and exploitation schemes.
+ """
+ # Create a single new sample from each AL strategy
+ tradeoff_schemes = [None, 'equal', 'epsilon-decreasing', 'adaptive']
+ #sampling_method = ['random', 'latin-hypercube', 'sobol', 'halton',
+ # 'hammersley', 'chebyshev', 'grid']
+ exploration_schemes = ['Voronoi', 'global_mc', 'random', 'latin-hypercube', 'LOOCV',
+ 'dual annealing']
+ exploration_schemes = ['global_mc', 'random', 'latin-hypercube', 'LOOCV',
+ 'dual annealing']
+ exploration_schemes = ['random', 'dual annealing']
+ exploitation_schemes = ['BayesOptDesign', 'BayesActDesign', 'VarOptDesign',
+ 'alphabetic', 'Space-filling']
+ exploitation_schemes = ['BayesActDesign', 'alphabetic', 'Space-filling']
+
+ for tradeoff in tradeoff_schemes:
+ for exploration in exploration_schemes:
+ for exploitation in exploitation_schemes:
+ if exploration == 'dual annealing':
+ if exploitation not in ['BayesOptDesign','VarOptDesign']:
+ continue
+
+ # Utility function depends on exploitation type
+ if exploitation == 'BayesOptDesign':
+ # 1) MI (Mutual information) 2) ALC (Active learning McKay)
+ # 2)DKL (Kullback-Leibler Divergence) 3)DPP (D-Posterior-percision)
+ # 4)APP (A-Posterior-percision) # ['DKL', 'BME', 'infEntropy']
+ util_func_list = ['MI', 'ALC', 'DKL', 'DPP', 'APP',
+ 'BayesRisk', 'infEntropy']
+ elif exploitation == 'BayesActDesign':
+ # 1) BME (Bayesian model evidence)
+ # 2) infEntropy (Information entropy)
+ # 2)DKL (Kullback-Leibler Divergence)
+ util_func_list = ['BME', 'DKL', 'infEntropy', 'BIC',
+ 'AIC', 'DIC']
+ elif exploitation == 'VarOptDesign':
+ # 1)ALM 2)EIGF, 3)LOOCV
+ # or a combination as a list
+ util_func_list = ['ALM', 'EIGF', 'LOOCV']
+ elif exploitation == 'alphabetic':
+ # 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
+ # 3)K-Opt (K-Optimality) or a combination as a list
+ util_func_list = ['D-Opt', 'A-Opt', 'K-Opt']
+ else:
+ util_func_list = ['']
+
+ for util in util_func_list:
+ # Stop the not working ones
+ if exploitation == 'BayesActDesign' and util == 'DIC':
+ continue
+ # General setting reset and update
+ engine.ExpDesign.n_max_samples = engine.ExpDesign.X.shape[0]+1
+
+ # Iteration-specific settings
+ engine.ExpDesign.tradeoff_scheme = tradeoff
+ ExpDesign.sampling_method = 'latin_hypercube'
+ ExpDesign.explore_method = exploration
+ ExpDesign.exploit_method = exploitation
+ engine.ExpDesign.util_func = util
+
+ # Do the Sequential training
+ print('')
+ print('*'*50)
+ print('Current settings:')
+ print(f' - tradeoff: {tradeoff}')
+ print(f' - exploration: {exploration}')
+ print(f' - exploitation: {exploitation}')
+ print(f' - util_func: {util}')
+ engine.train_sequential()
+
+ # Run through all types of AL for 1 iteration each to check their functionality
+ #engine.train_sequential()
+
+ # Load the objects
+ # with open(f"PCEModel_{Model.name}.pkl", "rb") as input:
+ # PCEModel = joblib.load(input)
+
+#%%
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ PostPCE = PostProcessing(engine)
+
+ # Plot to check validation visually.
+ PostPCE.valid_metamodel(n_samples=1)
+
+ # Compute and print RMSE error
+ PostPCE.check_accuracy(n_samples=300)
+
+ # Compute the moments and compare with the Monte-Carlo reference
+ if MetaModelOpts.meta_model_type != 'GPE':
+ PostPCE.plot_moments()
+
+ # Plot the evolution of the KLD,BME, and Modified LOOCV error
+ if MetaModelOpts.ExpDesign.method == 'sequential':
+ refBME_KLD = np.load("data/refBME_KLD_"+str(ndim)+".npy")
+ PostPCE.plot_seq_design_diagnostics(refBME_KLD)
+
+ # Plot the sobol indices
+ if MetaModelOpts.meta_model_type != 'GPE':
+ total_sobol = PostPCE.sobol_indices()
+
+ # =====================================================
+ # ======== Bayesian inference with Emulator ==========
+ # =====================================================
+ BayesOpts = BayesInference(engine)
+ BayesOpts.emulator = True
+ BayesOpts.plot_post_pred = True
+
+ # BayesOpts.selected_indices = [0, 3, 5, 7, 9]
+ # BME Bootstrap
+ BayesOpts.bootstrap = True
+ BayesOpts.n_bootstrap_itrs = 500
+ BayesOpts.bootstrap_noise = 100
+
+ # Bayesian cross validation
+ BayesOpts.bayes_loocv = True # TODO: test what this does
+
+ # Select the inference method
+ import emcee
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters passed to self.mcmc_params
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e4,#5,
+ 'n_walkers': 30,
+ 'moves': emcee.moves.KDEMove(),
+ 'multiprocessing': False,
+ 'verbose': False
+ }
+
+ # ----- Define the discrepancy model -------
+ obsData = pd.DataFrame(Model.observations, columns=Model.Output.names)
+ BayesOpts.measurement_error = obsData
+
+ # # -- (Option B) --
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obsData**2
+ BayesOpts.Discrepancy = DiscrepancyOpts
+
+ # -- (Option C) --
+ if 0:
+ DiscOutputOpts = Input()
+ # # # OutputName = 'Z'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[0].Nnme = '$\sigma^2_{\epsilon}$'
+ DiscOutputOpts.Marginals[0].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[0].parameters = [0, 10]
+ #BayesOpts.Discrepancy = {'known': DiscrepancyOpts,
+ # 'infer': Discrepancy(DiscOutputOpts)}
+
+ BayesOpts.bias_inputs = {'Z':np.arange(0, 10, 1.).reshape(-1,1) / 9}
+
+ DiscOutputOpts = Input()
+ # OutputName = 'lambda'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[0].name = '$\lambda$'
+ DiscOutputOpts.Marginals[0].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[0].parameters = [0, 1]
+
+ # # OutputName = 'sigma_f'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[1].Name = '$\sigma_f$'
+ DiscOutputOpts.Marginals[1].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[1].parameters = [0, 1e-4]
+ #BayesOpts.Discrepancy = Discrepancy(DiscOutputOpts)
+ BayesOpts.Discrepancy = {'known': DiscrepancyOpts,
+ 'infer': Discrepancy(DiscOutputOpts)}
+
+ # Start the calibration/inference
+ Bayes_PCE = BayesOpts.create_inference()
+
+ # Save class objects
+ with open(f'Bayes_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(Bayes_PCE, output, 2)
diff --git a/src/bayesvalidrox.egg-info/SOURCES.txt b/src/bayesvalidrox.egg-info/SOURCES.txt
index 1095272eae0e9115435ccb2a9c66f21241477066..5fdca7b71e2a4f6396d9876cd57f95a7690f566d 100644
--- a/src/bayesvalidrox.egg-info/SOURCES.txt
+++ b/src/bayesvalidrox.egg-info/SOURCES.txt
@@ -32,6 +32,7 @@ src/bayesvalidrox/surrogate_models/inputs.py
src/bayesvalidrox/surrogate_models/orthogonal_matching_pursuit.py
src/bayesvalidrox/surrogate_models/reg_fast_ard.py
src/bayesvalidrox/surrogate_models/reg_fast_laplace.py
+src/bayesvalidrox/surrogate_models/sequential_design.py
src/bayesvalidrox/surrogate_models/surrogate_models.py
tests/test_BayesInference.py
tests/test_BayesModelComparison.py
@@ -42,6 +43,7 @@ tests/test_Input.py
tests/test_InputSpace.py
tests/test_MCMC.py
tests/test_MetaModel.py
+tests/test_SequentialDesign.py
tests/test_engine.py
tests/test_polyconst.py
tests/test_pylink.py
\ No newline at end of file
diff --git a/src/bayesvalidrox/bayes_inference/bayes_inference.py b/src/bayesvalidrox/bayes_inference/bayes_inference.py
index e6748a87839a4a8448ac9a19a42dba84970fc56e..5bc144960907c7dbdd8fffa2587453d9c8f246f3 100644
--- a/src/bayesvalidrox/bayes_inference/bayes_inference.py
+++ b/src/bayesvalidrox/bayes_inference/bayes_inference.py
@@ -1410,7 +1410,7 @@ class BayesInference:
for xi in range(yi):
ax = axes[yi, xi]
ax.set_xlim(self.engine.ExpDesign.bound_tuples[xi])
- plt.close()
+
# Turn off gridlines
for ax in figPosterior.axes:
@@ -1425,7 +1425,7 @@ class BayesInference:
figPosterior.savefig(f'./{self.out_dir}{plotname}.pdf',
bbox_inches='tight')
- plt.clf()
+ plt.close()
def plot_log_BME(self):
"""
diff --git a/src/bayesvalidrox/post_processing/post_processing.py b/src/bayesvalidrox/post_processing/post_processing.py
index 6520a40f9f2393798f6b8abac026b9ed38fe33ca..50b32dbea7effb358a5e47835a9002efa97587c8 100644
--- a/src/bayesvalidrox/post_processing/post_processing.py
+++ b/src/bayesvalidrox/post_processing/post_processing.py
@@ -244,14 +244,14 @@ class PostProcessing:
" of samples!")
# Generate random samples if necessary
- Samples = self._get_sample() if samples is None else samples
+ samples = self._get_sample() if samples is None else samples
# Run the original model with the generated samples
if outputs is None:
- outputs = self._eval_model(Samples, key_str='validSet')
+ outputs = self._eval_model(samples, key_str='validSet')
# Run the PCE model with the generated samples
- pce_outputs, _ = MetaModel.eval_metamodel(samples=Samples)
+ pce_outputs, _ = MetaModel.eval_metamodel(samples=samples)
self.rmse = {}
self.valid_error = {}
@@ -321,6 +321,7 @@ class PostProcessing:
if len(name_util) == 0:
continue
+ print(seq_dict)
# Box plot when Replications have been detected.
if any(int(name.split("rep_", 1)[1]) > 1 for name in name_util):
@@ -493,6 +494,8 @@ class PostProcessing:
seq_values = np.nan_to_num(seq_values)
# Plot the error evolution for each output
+ print(x_idx.shape)
+ print(seq_values.mean(axis=1).shape)
plt.semilogy(x_idx, seq_values.mean(axis=1),
marker=markers[idx], ls='--', lw=2,
color=colors[idx],
diff --git a/src/bayesvalidrox/surrogate_models/engine.py b/src/bayesvalidrox/surrogate_models/engine.py
index 086022ab042f66aa1f640ba6ad8bd5ebc19fb9b8..ab0aaeea564c95f169fac2a0e47428bbd43c7491 100644
--- a/src/bayesvalidrox/surrogate_models/engine.py
+++ b/src/bayesvalidrox/surrogate_models/engine.py
@@ -25,108 +25,7 @@ from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
from .exploration import Exploration
from.surrogate_models import MetaModel as MM
from.surrogate_models import create_psi
-
-
-def hellinger_distance(P, Q):
- """
- Hellinger distance between two continuous distributions.
-
- The maximum distance 1 is achieved when P assigns probability zero to
- every set to which Q assigns a positive probability, and vice versa.
- 0 (identical) and 1 (maximally different)
-
- Parameters
- ----------
- P : array
- Reference likelihood.
- Q : array
- Estimated likelihood.
-
- Returns
- -------
- float
- Hellinger distance of two distributions.
-
- """
- P = np.array(P)
- Q = np.array(Q)
-
- mu1 = P.mean()
- Sigma1 = np.std(P)
-
- mu2 = Q.mean()
- Sigma2 = np.std(Q)
-
- term1 = np.sqrt(2 * Sigma1 * Sigma2 / (Sigma1 ** 2 + Sigma2 ** 2))
-
- term2 = np.exp(-.25 * (mu1 - mu2) ** 2 / (Sigma1 ** 2 + Sigma2 ** 2))
-
- H_squared = 1 - term1 * term2
-
- return np.sqrt(H_squared)
-
-
-def logpdf(x, mean, cov):
- """
- Computes the likelihood based on a multivariate normal distribution.
-
- Parameters
- ----------
- x : TYPE
- DESCRIPTION.
- mean : array_like
- Observation data.
- cov : 2d array
- Covariance matrix of the distribution.
-
- Returns
- -------
- log_lik : float
- Log likelihood.
-
- """
- n = len(mean)
- L = linalg.cholesky(cov, lower=True)
- beta = np.sum(np.log(np.diag(L)))
- dev = x - mean
- alpha = dev.dot(linalg.cho_solve((L, True), dev))
- log_lik = -0.5 * alpha - beta - n / 2. * np.log(2 * np.pi)
-
- return log_lik
-
-
-def subdomain(Bounds, n_new_samples):
- """
- Divides a domain defined by Bounds into subdomains.
-
- Parameters
- ----------
- Bounds : list of tuples
- List of lower and upper bounds.
- n_new_samples : int
- Number of samples to divide the domain for.
-
- Returns
- -------
- Subdomains : List of tuples of tuples
- Each tuple of tuples divides one set of bounds into n_new_samples parts.
-
- """
- n_params = len(Bounds)
- n_subdomains = n_new_samples + 1
- LinSpace = np.zeros((n_params, n_subdomains))
-
- for i in range(n_params):
- LinSpace[i] = np.linspace(start=Bounds[i][0], stop=Bounds[i][1],
- num=n_subdomains)
- Subdomains = []
- for k in range(n_subdomains - 1):
- mylist = []
- for i in range(n_params):
- mylist.append((LinSpace[i, k + 0], LinSpace[i, k + 1]))
- Subdomains.append(tuple(mylist))
-
- return Subdomains
+from .sequential_design import SequentialDesign, hellinger_distance, logpdf, subdomain
class Engine:
@@ -155,6 +54,7 @@ class Engine:
self.valid_likelihoods = None
self._y_hat_prev = None
self.emulator = False
+ self.verbose = False
def start_engine(self) -> None:
"""
@@ -169,10 +69,12 @@ class Engine:
if isinstance(self.MetaModel, MM):
self.emulator = True
self.MetaModel.out_names = self.out_names
- print('MetaModel has been given, `emulator` will be set to `True`')
+ if self.verbose:
+ print('MetaModel has been given, `emulator` will be set to `True`')
else:
self.emulator = False
- print('MetaModel has not been given, `emulator` will be set to `False`')
+ if self.verbose:
+ print('MetaModel has not been given, `emulator` will be set to `False`')
def train_normal(self, parallel=False, verbose=False, save=False) -> None:
"""
@@ -187,6 +89,7 @@ class Engine:
None
"""
+ self.verbose = verbose
self.start_engine()
ExpDesign = self.ExpDesign
@@ -230,7 +133,8 @@ class Engine:
ExpDesign.x_values = ExpDesign.Y['x_values']
del ExpDesign.Y['x_values']
else:
- print('No x_values are given, this might lead to issues during PostProcessing')
+ if self.verbose:
+ print('No x_values are given, this might lead to issues during PostProcessing')
# Fit the surrogate
if self.emulator:
@@ -361,7 +265,8 @@ class Engine:
pce = True
else:
pce = False
- mc_ref = True if bool(self.Model.mc_reference) else False
+ #mc_ref = True if bool(self.Model.mc_reference) else False
+ mc_ref = True if (self.Model.mc_reference is not None) else False
if mc_ref:
self.Model.read_observation('mc_ref')
@@ -374,6 +279,10 @@ class Engine:
util_func = self.ExpDesign.util_func
output_name = self.out_names
+ # Setup the Sequential Design object
+ self.SeqDes = SequentialDesign(self.MetaModel, self.Model, self.ExpDesign, self)
+ self.SeqDes.out_names = self.out_names
+
# Handle if only one UtilityFunctions is provided
if not isinstance(util_func, list):
util_func = [self.ExpDesign.util_func]
@@ -502,17 +411,30 @@ class Engine:
# Save the metamodel prediction before updating
prevMetaModel_dict[itr_no] = deepcopy(self.MetaModel)
# prevExpDesign_dict[itr_no] = deepcopy(self.ExpDesign)
+ # TODO: recheck that the iteration numbers here match what it should do!
if itr_no > 1:
pc_model = prevMetaModel_dict[itr_no - 1]
- self._y_hat_prev, _ = pc_model.eval_metamodel(
+ self.SeqDes._y_hat_prev, _ = pc_model.eval_metamodel(
samples=Xfull[-1].reshape(1, -1))
del prevMetaModel_dict[itr_no - 1]
+ if itr_no == 1 and self.ExpDesign.tradeoff_scheme == 'adaptive':
+ # TODO: this was added just as a fix, needs to be reworked
+ # Changes: itr_no-1 -> itr_no
+ # Xfull[-1] -> Xprev
+ #print(Xprev.shape)
+ pc_model = prevMetaModel_dict[itr_no]
+ self.SeqDes._y_hat_prev, _ = pc_model.eval_metamodel(
+ samples=Xprev)
# Optimal Bayesian Design
# self.MetaModel.ExpDesignFlag = 'sequential'
- Xnew, updatedPrior = self.choose_next_sample(TotalSigma2,
+ Xnew, updatedPrior = self.SeqDes.choose_next_sample(TotalSigma2,
n_canddidate,
util_f)
+
+# Xnew, updatedPrior = self.choose_next_sample(TotalSigma2,
+# n_canddidate,
+# util_f)
S = np.min(distance.cdist(Xinit, Xnew, 'euclidean'))
self.seqMinDist.append(S)
print(f"\nmin Dist from OldExpDesign: {S:2f}")
@@ -678,1177 +600,6 @@ class Engine:
# return self.MetaModel
- # -------------------------------------------------------------------------
- def util_VarBasedDesign(self, X_can, index, util_func='Entropy'):
- """
- Computes the exploitation scores based on:
- active learning MacKay(ALM) and active learning Cohn (ALC)
- Paper: Sequential Design with Mutual Information for Computer
- Experiments (MICE): Emulation of a Tsunami Model by Beck and Guillas
- (2016)
-
- Parameters
- ----------
- X_can : array of shape (n_samples, n_params)
- Candidate samples.
- index : int
- Model output index.
- util_func : string, optional
- Exploitation utility function. The default is 'Entropy'.
-
- Returns
- -------
- float
- Score.
-
- """
- MetaModel = self.MetaModel
- ED_X = self.ExpDesign.X
- out_dict_y = self.ExpDesign.Y
- out_names = self.out_names
-
- # Run the Metamodel for the candidate
- X_can = X_can.reshape(1, -1)
- Y_PC_can, std_PC_can = MetaModel.eval_metamodel(samples=X_can)
-
- score = None
- if util_func.lower() == 'alm':
- # ----- Entropy/MMSE/active learning MacKay(ALM) -----
- # Compute perdiction variance of the old model
- canPredVar = {key: std_PC_can[key] ** 2 for key in out_names}
-
- varPCE = np.zeros((len(out_names), X_can.shape[0]))
- for KeyIdx, key in enumerate(out_names):
- varPCE[KeyIdx] = np.max(canPredVar[key], axis=1)
- score = np.max(varPCE, axis=0)
-
- elif util_func.lower() == 'eigf':
- # ----- Expected Improvement for Global fit -----
- # Find closest EDX to the candidate
- distances = distance.cdist(ED_X, X_can, 'euclidean')
- index = np.argmin(distances)
-
- # Compute perdiction error and variance of the old model
- predError = {key: Y_PC_can[key] for key in out_names}
- canPredVar = {key: std_PC_can[key] ** 2 for key in out_names}
-
- # Compute perdiction error and variance of the old model
- # Eq (5) from Liu et al.(2018)
- EIGF_PCE = np.zeros((len(out_names), X_can.shape[0]))
- for KeyIdx, key in enumerate(out_names):
- residual = predError[key] - out_dict_y[key][int(index)]
- var = canPredVar[key]
- EIGF_PCE[KeyIdx] = np.max(residual ** 2 + var, axis=1)
- score = np.max(EIGF_PCE, axis=0)
-
- return -1 * score # -1 is for minimization instead of maximization
-
- # -------------------------------------------------------------------------
- def util_BayesianActiveDesign(self, y_hat, std, sigma2Dict, var='DKL'):
- """
- Computes scores based on Bayesian active design criterion (var).
-
- It is based on the following paper:
- Oladyshkin, Sergey, Farid Mohammadi, Ilja Kroeker, and Wolfgang Nowak.
- "Bayesian3 active learning for the gaussian process emulator using
- information theory." Entropy 22, no. 8 (2020): 890.
-
- Parameters
- ----------
- y_hat : unknown
- std : unknown
- sigma2Dict : dict
- A dictionary containing the measurement errors (sigma^2).
- var : string, optional
- BAL design criterion. The default is 'DKL'.
-
- Returns
- -------
- float
- Score.
-
- """
-
- # Get the data
- obs_data = self.observations
- # TODO: this should be optimizable to be calculated explicitly
- if hasattr(self.Model, 'n_obs'):
- n_obs = self.Model.n_obs
- else:
- n_obs = self.n_obs
- mc_size = 10000
-
- # Sample a distribution for a normal dist
- # with Y_mean_can as the mean and Y_std_can as std.
- Y_MC, std_MC = {}, {}
- logPriorLikelihoods = np.zeros(mc_size)
- for key in list(y_hat):
- cov = np.diag(std[key] ** 2)
- print(key, y_hat[key], std[key])
- # TODO: added the allow_singular = True here
- rv = stats.multivariate_normal(mean=y_hat[key], cov=cov, allow_singular=True)
- Y_MC[key] = rv.rvs(size=mc_size)
- logPriorLikelihoods += rv.logpdf(Y_MC[key])
- std_MC[key] = np.zeros((mc_size, y_hat[key].shape[0]))
-
- # Likelihood computation (Comparison of data and simulation
- # results via PCE with candidate design)
- print(Y_MC)
- likelihoods = self._normpdf(Y_MC, std_MC, obs_data, sigma2Dict)
-
- # Rejection Step
- # Random numbers between 0 and 1
- unif = np.random.rand(1, mc_size)[0]
-
- # Reject the poorly performed prior
- accepted = (likelihoods / np.max(likelihoods)) >= unif
-
- # Prior-based estimation of BME
- logBME = np.log(np.nanmean(likelihoods), dtype=np.longdouble) # float128)
-
- # Posterior-based expectation of likelihoods
- postLikelihoods = likelihoods[accepted]
- postExpLikelihoods = np.mean(np.log(postLikelihoods))
-
- # Posterior-based expectation of prior densities
- postExpPrior = np.mean(logPriorLikelihoods[accepted])
-
- # Utility function Eq.2 in Ref. (2)
- # Posterior covariance matrix after observing data y
- # Kullback-Leibler Divergence (Sergey's paper)
- U_J_d = None
- if var == 'DKL':
-
- # TODO: Calculate the correction factor for BME
- # BMECorrFactor = self.BME_Corr_Weight(PCE_SparseBayes_can,
- # ObservationData, sigma2Dict)
- # BME += BMECorrFactor
- # Haun et al implementation
- # U_J_d = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
- U_J_d = postExpLikelihoods - logBME
-
- # Marginal log likelihood
- elif var == 'BME':
- U_J_d = np.nanmean(likelihoods)
-
- # Entropy-based information gain
- elif var == 'infEntropy':
- logBME = np.log(np.nanmean(likelihoods))
- infEntropy = logBME - postExpPrior - postExpLikelihoods
- U_J_d = infEntropy * -1 # -1 for minimization
-
- # Bayesian information criterion
- elif var == 'BIC':
- coeffs = self.MetaModel.coeffs_dict.values()
- nModelParams = max(len(v) for val in coeffs for v in val.values())
- maxL = np.nanmax(likelihoods)
- U_J_d = -2 * np.log(maxL) + np.log(n_obs) * nModelParams
-
- # Akaike information criterion
- elif var == 'AIC':
- coeffs = self.MetaModel.coeffs_dict.values()
- nModelParams = max(len(v) for val in coeffs for v in val.values())
- maxlogL = np.log(np.nanmax(likelihoods))
- AIC = -2 * maxlogL + 2 * nModelParams
- # 2 * nModelParams * (nModelParams+1) / (n_obs-nModelParams-1)
- penTerm = 0
- U_J_d = 1 * (AIC + penTerm)
-
- # Deviance information criterion
- elif var == 'DIC':
- # D_theta_bar = np.mean(-2 * Likelihoods)
- N_star_p = 0.5 * np.var(np.log(likelihoods[likelihoods != 0]))
- Likelihoods_theta_mean = self._normpdf(
- y_hat, std, obs_data, sigma2Dict
- )
- DIC = -2 * np.log(Likelihoods_theta_mean) + 2 * N_star_p
-
- U_J_d = DIC
-
- else:
- print('The algorithm you requested has not been implemented yet!')
-
- # Handle inf and NaN (replace by zero)
- if np.isnan(U_J_d) or U_J_d == -np.inf or U_J_d == np.inf:
- U_J_d = 0.0
-
- # Clear memory
- del likelihoods
- del Y_MC
- del std_MC
-
- return -1 * U_J_d # -1 is for minimization instead of maximization
-
- # -------------------------------------------------------------------------
- def util_BayesianDesign(self, X_can, X_MC, sigma2Dict, var='DKL'):
- """
- Computes scores based on Bayesian sequential design criterion (var).
-
- Parameters
- ----------
- X_can : array of shape (n_samples, n_params)
- Candidate samples.
- X_MC : unknown
- sigma2Dict : dict
- A dictionary containing the measurement errors (sigma^2).
- var : string, optional
- Bayesian design criterion. The default is 'DKL'.
-
- Returns
- -------
- float
- Score.
-
- """
-
- # To avoid changes ub original aPCE object
- MetaModel = self.MetaModel
- out_names = self.out_names
- if X_can.ndim == 1:
- X_can = X_can.reshape(1, -1)
-
- # Compute the mean and std based on the MetaModel
- # pce_means, pce_stds = self._compute_pce_moments(MetaModel)
- if var == 'ALC':
- Y_MC, Y_MC_std = MetaModel.eval_metamodel(samples=X_MC)
-
- # Old Experimental design
- oldExpDesignX = self.ExpDesign.X
- oldExpDesignY = self.ExpDesign.Y
-
- # Evaluate the PCE metamodels at that location ???
- Y_PC_can, Y_std_can = MetaModel.eval_metamodel(samples=X_can)
- PCE_Model_can = deepcopy(MetaModel)
- engine_can = deepcopy(self)
- # Add the candidate to the ExpDesign
- NewExpDesignX = np.vstack((oldExpDesignX, X_can))
-
- NewExpDesignY = {}
- for key in oldExpDesignY.keys():
- NewExpDesignY[key] = np.vstack(
- (oldExpDesignY[key], Y_PC_can[key])
- )
-
- engine_can.ExpDesign.sampling_method = 'user'
- engine_can.ExpDesign.X = NewExpDesignX
- # engine_can.ModelOutputDict = NewExpDesignY
- engine_can.ExpDesign.Y = NewExpDesignY
-
- # Train the model for the observed data using x_can
- engine_can.MetaModel.input_obj.poly_coeffs_flag = False
- engine_can.start_engine()
- engine_can.train_normal(parallel=False)
- engine_can.MetaModel.fit(NewExpDesignX, NewExpDesignY)
- # engine_can.train_norm_design(parallel=False)
-
- # Set the ExpDesign to its original values
- engine_can.ExpDesign.X = oldExpDesignX
- engine_can.ModelOutputDict = oldExpDesignY
- engine_can.ExpDesign.Y = oldExpDesignY
-
- if var.lower() == 'mi':
- # Mutual information based on Krause et al.
- # Adapted from Beck & Guillas (MICE) paper
- _, std_PC_can = engine_can.MetaModel.eval_metamodel(samples=X_can)
- std_can = {key: std_PC_can[key] for key in out_names}
-
- std_old = {key: Y_std_can[key] for key in out_names}
-
- varPCE = np.zeros((len(out_names)))
- for i, key in enumerate(out_names):
- varPCE[i] = np.mean(std_old[key] ** 2 / std_can[key] ** 2)
- score = np.mean(varPCE)
-
- return -1 * score
-
- elif var.lower() == 'alc':
- # Active learning based on Gramyc and Lee
- # Adaptive design and analysis of supercomputer experiments Techno-
- # metrics, 51 (2009), pp. 130–145.
-
- # Evaluate the MetaModel at the given samples
- Y_MC_can, Y_MC_std_can = engine_can.MetaModel.eval_metamodel(samples=X_MC)
-
- # Compute the score
- score = []
- for i, key in enumerate(out_names):
- pce_var = Y_MC_std_can[key] ** 2
- pce_var_can = Y_MC_std[key] ** 2
- score.append(np.mean(pce_var - pce_var_can, axis=0))
- score = np.mean(score)
-
- return -1 * score
-
- # ---------- Inner MC simulation for computing Utility Value ----------
- # Estimation of the integral via Monte Varlo integration
- MCsize = X_MC.shape[0]
- ESS = 0
-
- likelihoods = None
- while (ESS > MCsize) or (ESS < 1):
-
- # Enriching Monte Carlo samples if need be
- if ESS != 0:
- X_MC = self.ExpDesign.generate_samples(
- MCsize, 'random'
- )
-
- # Evaluate the MetaModel at the given samples
- Y_MC, std_MC = PCE_Model_can.eval_metamodel(samples=X_MC)
-
- # Likelihood computation (Comparison of data and simulation
- # results via PCE with candidate design)
- likelihoods = self._normpdf(
- Y_MC, std_MC, self.observations, sigma2Dict
- )
-
- # Check the Effective Sample Size (1<ESS<MCsize)
- ESS = 1 / np.sum(np.square(likelihoods / np.sum(likelihoods)))
-
- # Enlarge sample size if it doesn't fulfill the criteria
- if (ESS > MCsize) or (ESS < 1):
- print("--- increasing MC size---")
- MCsize *= 10
- ESS = 0
-
- # Rejection Step
- # Random numbers between 0 and 1
- unif = np.random.rand(1, MCsize)[0]
-
- # Reject the poorly performed prior
- accepted = (likelihoods / np.max(likelihoods)) >= unif
-
- # -------------------- Utility functions --------------------
- # Utility function Eq.2 in Ref. (2)
- # Kullback-Leibler Divergence (Sergey's paper)
- U_J_d = None
- if var == 'DKL':
-
- # Prior-based estimation of BME
- logBME = np.log(np.nanmean(likelihoods, dtype=np.longdouble)) # float128))
-
- # Posterior-based expectation of likelihoods
- # postLikelihoods = likelihoods[accepted]
- # postExpLikelihoods = np.mean(np.log(postLikelihoods))
-
- # Haun et al implementation
- U_J_d = np.mean(np.log(likelihoods[likelihoods != 0]) - logBME)
-
- # U_J_d = np.sum(G_n_m_all)
- # Ryan et al (2014) implementation
- # importanceWeights = Likelihoods[Likelihoods!=0]/np.sum(Likelihoods[Likelihoods!=0])
- # U_J_d = np.mean(importanceWeights*np.log(Likelihoods[Likelihoods!=0])) - logBME
-
- # U_J_d = postExpLikelihoods - logBME
-
- # Marginal likelihood
- elif var == 'BME':
-
- # Prior-based estimation of BME
- logBME = np.log(np.nanmean(likelihoods))
- U_J_d = logBME
-
- # Bayes risk likelihood
- elif var == 'BayesRisk':
-
- U_J_d = -1 * np.var(likelihoods)
-
- # Entropy-based information gain
- elif var == 'infEntropy':
- # Prior-based estimation of BME
- logBME = np.log(np.nanmean(likelihoods))
-
- # Posterior-based expectation of likelihoods
- postLikelihoods = likelihoods[accepted]
- postLikelihoods /= np.nansum(likelihoods[accepted])
- postExpLikelihoods = np.mean(np.log(postLikelihoods))
-
- # Posterior-based expectation of prior densities
- logPriorLikelihoods = []
- logPriorLikelihoods[accepted] = None # TODO: this is not defined here, just a fix
- postExpPrior = np.mean(logPriorLikelihoods[accepted])
-
- infEntropy = logBME - postExpPrior - postExpLikelihoods
-
- U_J_d = infEntropy * -1 # -1 for minimization
-
- # D-Posterior-precision
- elif var == 'DPP':
- X_Posterior = X_MC[accepted]
- # covariance of the posterior parameters
- U_J_d = -np.log(np.linalg.det(np.cov(X_Posterior)))
-
- # A-Posterior-precision
- elif var == 'APP':
- X_Posterior = X_MC[accepted]
- # trace of the posterior parameters
- U_J_d = -np.log(np.trace(np.cov(X_Posterior)))
-
- else:
- print('The algorithm you requested has not been implemented yet!')
-
- # Clear memory
- del likelihoods
- del Y_MC
- del std_MC
-
- return -1 * U_J_d # -1 is for minimization instead of maximization
-
- # -------------------------------------------------------------------------
- def run_util_func(self, method, candidates, index, sigma2Dict=None,
- var=None, X_MC=None):
- """
- Runs the utility function based on the given method.
-
- Parameters
- ----------
- method : string
- Exploitation method: `VarOptDesign`, `BayesActDesign` and
- `BayesOptDesign`.
- candidates : array of shape (n_samples, n_params)
- All candidate parameter sets.
- index : int
- ExpDesign index.
- sigma2Dict : dict, optional
- A dictionary containing the measurement errors (sigma^2). The
- default is None.
- var : string, optional
- Utility function. The default is None.
- X_MC : TYPE, optional
- DESCRIPTION. The default is None.
-
- Returns
- -------
- index : TYPE
- DESCRIPTION.
- List
- Scores.
-
- """
-
- if method.lower() == 'varoptdesign':
- # U_J_d = self.util_VarBasedDesign(candidates, index, var)
- U_J_d = np.zeros((candidates.shape[0]))
- for idx, X_can in tqdm(enumerate(candidates), ascii=True,
- desc="varoptdesign"):
- U_J_d[idx] = self.util_VarBasedDesign(X_can, index, var)
-
- elif method.lower() == 'bayesactdesign':
- NCandidate = candidates.shape[0]
- U_J_d = np.zeros(NCandidate)
- # Evaluate all candidates
- y_can, std_can = self.MetaModel.eval_metamodel(samples=candidates)
- # loop through candidates
- for idx, X_can in tqdm(enumerate(candidates), ascii=True,
- desc="BAL Design"):
- y_hat = {key: items[idx] for key, items in y_can.items()}
- std = {key: items[idx] for key, items in std_can.items()}
-
- # print(y_hat)
- # print(std)
- U_J_d[idx] = self.util_BayesianActiveDesign(
- y_hat, std, sigma2Dict, var)
-
- elif method.lower() == 'bayesoptdesign':
- NCandidate = candidates.shape[0]
- U_J_d = np.zeros(NCandidate)
- for idx, X_can in tqdm(enumerate(candidates), ascii=True,
- desc="OptBayesianDesign"):
- U_J_d[idx] = self.util_BayesianDesign(X_can, X_MC, sigma2Dict,
- var)
- return index, -1 * U_J_d
-
- # -------------------------------------------------------------------------
- def dual_annealing(self, method, Bounds, sigma2Dict, var, Run_No,
- verbose=False):
- """
- Exploration algorithm to find the optimum parameter space.
-
- Parameters
- ----------
- method : string
- Exploitation method: `VarOptDesign`, `BayesActDesign` and
- `BayesOptDesign`.
- Bounds : list of tuples
- List of lower and upper boundaries of parameters.
- sigma2Dict : dict
- A dictionary containing the measurement errors (sigma^2).
- var : unknown
- Run_No : int
- Run number.
- verbose : bool, optional
- Print out a summary. The default is False.
-
- Returns
- -------
- Run_No : int
- Run number.
- array
- Optimial candidate.
-
- """
-
- Model = self.Model
- max_func_itr = self.ExpDesign.max_func_itr
-
- Res_Global = None
- if method.lower() == 'varoptdesign':
- Res_Global = opt.dual_annealing(self.util_VarBasedDesign,
- bounds=Bounds,
- args=(Model, var),
- maxfun=max_func_itr)
-
- elif method.lower() == 'bayesoptdesign':
- Res_Global = opt.dual_annealing(self.util_BayesianDesign,
- bounds=Bounds,
- args=(Model, sigma2Dict, var),
- maxfun=max_func_itr)
-
- if verbose:
- print(f"Global minimum: xmin = {Res_Global.x}, "
- f"f(xmin) = {Res_Global.fun:.6f}, nfev = {Res_Global.nfev}")
-
- return Run_No, Res_Global.x
-
- # -------------------------------------------------------------------------
- def tradeoff_weights(self, tradeoff_scheme, old_EDX, old_EDY):
- """
- Calculates weights for exploration scores based on the requested
- scheme: `None`, `equal`, `epsilon-decreasing` and `adaptive`.
-
- `None`: No exploration.
- `equal`: Same weights for exploration and exploitation scores.
- `epsilon-decreasing`: Start with more exploration and increase the
- influence of exploitation along the way with an exponential decay
- function
- `adaptive`: An adaptive method based on:
- Liu, Haitao, Jianfei Cai, and Yew-Soon Ong. "An adaptive sampling
- approach for Kriging metamodeling by maximizing expected prediction
- error." Computers & Chemical Engineering 106 (2017): 171-182.
-
- Parameters
- ----------
- tradeoff_scheme : string
- Trade-off scheme for exloration and exploitation scores.
- old_EDX : array (n_samples, n_params)
- Old experimental design (training points).
- old_EDY : dict
- Old model responses (targets).
-
- Returns
- -------
- exploration_weight : float
- Exploration weight.
- exploitation_weight: float
- Exploitation weight.
-
- """
- exploration_weight = None
-
- if tradeoff_scheme is None:
- exploration_weight = 0
-
- elif tradeoff_scheme == 'equal':
- exploration_weight = 0.5
-
- elif tradeoff_scheme == 'epsilon-decreasing':
- # epsilon-decreasing scheme
- # Start with more exploration and increase the influence of
- # exploitation along the way with an exponential decay function
- initNSamples = self.ExpDesign.n_init_samples
- n_max_samples = self.ExpDesign.n_max_samples
-
- itrNumber = (self.ExpDesign.X.shape[0] - initNSamples)
- itrNumber //= self.ExpDesign.n_new_samples
-
- tau2 = -(n_max_samples - initNSamples - 1) / np.log(1e-8)
- exploration_weight = signal.windows.exponential(n_max_samples - initNSamples,
- 0, tau2, False)[itrNumber]
-
- elif tradeoff_scheme == 'adaptive':
-
- # Extract itrNumber
- initNSamples = self.ExpDesign.n_init_samples
- # n_max_samples = self.ExpDesign.n_max_samples
- itrNumber = (self.ExpDesign.X.shape[0] - initNSamples)
- itrNumber //= self.ExpDesign.n_new_samples
-
- if itrNumber == 0:
- exploration_weight = 0.5
- else:
- # New adaptive trade-off according to Liu et al. (2017)
- # Mean squared error for last design point
- last_EDX = old_EDX[-1].reshape(1, -1)
- lastPCEY, _ = self.MetaModel.eval_metamodel(samples=last_EDX)
- pce_y = np.array(list(lastPCEY.values()))[:, 0]
- y = np.array(list(old_EDY.values()))[:, -1, :]
- mseError = mean_squared_error(pce_y, y)
-
- # Mean squared CV - error for last design point
- pce_y_prev = np.array(list(self._y_hat_prev.values()))[:, 0]
- mseCVError = mean_squared_error(pce_y_prev, y)
-
- exploration_weight = min([0.5 * mseError / mseCVError, 1])
-
- # Exploitation weight
- exploitation_weight = 1 - exploration_weight
-
- return exploration_weight, exploitation_weight
-
- # -------------------------------------------------------------------------
- def choose_next_sample(self, sigma2=None, n_candidates=5, var='DKL'):
- """
- Runs optimal sequential design.
-
- Parameters
- ----------
- sigma2 : dict, optional
- A dictionary containing the measurement errors (sigma^2). The
- default is None.
- n_candidates : int, optional
- Number of candidate samples. The default is 5.
- var : string, optional
- Utility function. The default is None. # TODO: default is set to DKL, not none
-
- Raises
- ------
- NameError
- Wrong utility function.
-
- Returns
- -------
- Xnew : array (n_samples, n_params)
- Selected new training point(s).
- """
-
- # Initialization
- Bounds = self.ExpDesign.bound_tuples
- n_new_samples = self.ExpDesign.n_new_samples
- explore_method = self.ExpDesign.explore_method
- exploit_method = self.ExpDesign.exploit_method
- n_cand_groups = self.ExpDesign.n_cand_groups
- tradeoff_scheme = self.ExpDesign.tradeoff_scheme
-
- old_EDX = self.ExpDesign.X
- old_EDY = self.ExpDesign.Y.copy()
- ndim = self.ExpDesign.X.shape[1]
- OutputNames = self.out_names
-
- # -----------------------------------------
- # ----------- CUSTOMIZED METHODS ----------
- # -----------------------------------------
- # Utility function exploit_method provided by user
- if exploit_method.lower() == 'user':
- # TODO: is the exploit_method meant here?
- if not hasattr(self.ExpDesign, 'ExploitFunction') or self.ExpDesign.ExploitFunction is None:
- raise AttributeError(
- 'Function `ExploitFunction` not given to the ExpDesign, thus cannor run user-defined sequential'
- 'scheme')
- # TODO: syntax does not fully match the rest - can test this??
- Xnew, filteredSamples = self.ExpDesign.ExploitFunction(self)
-
- print("\n")
- print("\nXnew:\n", Xnew)
-
- return Xnew, filteredSamples
-
- # Dual-Annealing works differently from the rest, so deal with this first
- # Here exploration and exploitation are performed simulataneously
- if explore_method == 'dual annealing':
- # ------- EXPLORATION: OPTIMIZATION -------
- import time
- start_time = time.time()
-
- # Divide the domain to subdomains
- subdomains = subdomain(Bounds, n_new_samples)
-
- # Multiprocessing
- if self.parallel:
- args = []
- for i in range(n_new_samples):
- args.append((exploit_method, subdomains[i], sigma2, var, i))
- pool = multiprocessing.Pool(multiprocessing.cpu_count())
-
- # With Pool.starmap_async()
- results = pool.starmap_async(self.dual_annealing, args).get()
-
- # Close the pool
- pool.close()
- # Without multiprocessing
- else:
- results = []
- for i in range(n_new_samples):
- results.append(self.dual_annealing(exploit_method, subdomains[i], sigma2, var, i))
-
- # New sample
- Xnew = np.array([results[i][1] for i in range(n_new_samples)])
- print("\nXnew:\n", Xnew)
-
- # Computational cost
- elapsed_time = time.time() - start_time
- print("\n")
- print(f"Elapsed_time: {round(elapsed_time, 2)} sec.")
- print('-' * 20)
-
- return Xnew, None
-
- # Generate needed Exploration class
- explore = Exploration(self.ExpDesign, n_candidates)
- explore.w = 100 # * ndim #500 # TODO: where does this value come from?
-
- # Select criterion (mc-intersite-proj-th, mc-intersite-proj)
- explore.mc_criterion = 'mc-intersite-proj'
-
- # Generate the candidate samples
- # TODO: here use the sampling method provided by the expdesign?
- # sampling_method = self.ExpDesign.sampling_method
-
- # TODO: changed this from 'random' for LOOCV
- # TODO: these are commented out as they are not used !?
- # if explore_method == 'LOOCV':
- # allCandidates = self.ExpDesign.generate_samples(n_candidates,
- # sampling_method)
- # else:
- # allCandidates, scoreExploration = explore.get_exploration_samples()
-
- # -----------------------------------------
- # ---------- EXPLORATION METHODS ----------
- # -----------------------------------------
- if explore_method == 'LOOCV':
- # -----------------------------------------------------------------
- # TODO: LOOCV model construnction based on Feng et al. (2020)
- # 'LOOCV':
- # Initilize the ExploitScore array
-
- # Generate random samples
- allCandidates = self.ExpDesign.generate_samples(n_candidates,
- 'random')
-
- # Construct error model based on LCerror
- errorModel = self.MetaModel.create_ModelError(old_EDX, self.LCerror)
- self.errorModel.append(copy(errorModel))
-
- # Evaluate the error models for allCandidates
- eLCAllCands, _ = errorModel.eval_errormodel(allCandidates)
- # Select the maximum as the representative error
- eLCAllCands = np.dstack(eLCAllCands.values())
- eLCAllCandidates = np.max(eLCAllCands, axis=1)[:, 0]
-
- # Normalize the error w.r.t the maximum error
- scoreExploration = eLCAllCandidates / np.sum(eLCAllCandidates)
-
- else:
- # ------- EXPLORATION: SPACE-FILLING DESIGN -------
- # Generate candidate samples from Exploration class
- explore = Exploration(self.ExpDesign, n_candidates)
- explore.w = 100 # * ndim #500
- # Select criterion (mc-intersite-proj-th, mc-intersite-proj)
- explore.mc_criterion = 'mc-intersite-proj'
- allCandidates, scoreExploration = explore.get_exploration_samples()
-
- # Temp: ---- Plot all candidates -----
- if ndim == 2:
- def plotter(points, allCandidates, Method,
- scoreExploration=None):
- """
- unknown
-
- Parameters
- ----------
- points
- allCandidates
- Method
- scoreExploration
-
- Returns
- -------
-
- """
- if Method == 'Voronoi':
- from scipy.spatial import Voronoi, voronoi_plot_2d
- vor = Voronoi(points)
- fig = voronoi_plot_2d(vor)
- ax1 = fig.axes[0]
- else:
- fig = plt.figure()
- ax1 = fig.add_subplot(111)
- ax1.scatter(points[:, 0], points[:, 1], s=10, c='r',
- marker="s", label='Old Design Points')
- ax1.scatter(allCandidates[:, 0], allCandidates[:, 1], s=10,
- c='b', marker="o", label='Design candidates')
- for i in range(points.shape[0]):
- txt = 'p' + str(i + 1)
- ax1.annotate(txt, (points[i, 0], points[i, 1]))
- if scoreExploration is not None:
- for i in range(allCandidates.shape[0]):
- txt = str(round(scoreExploration[i], 5))
- ax1.annotate(txt, (allCandidates[i, 0],
- allCandidates[i, 1]))
-
- plt.xlim(self.bound_tuples[0])
- plt.ylim(self.bound_tuples[1])
- # plt.show()
- plt.legend(loc='upper left')
-
- # -----------------------------------------
- # --------- EXPLOITATION METHODS ----------
- # -----------------------------------------
- if exploit_method.lower() == 'bayesoptdesign' or \
- exploit_method.lower() == 'bayesactdesign':
-
- # ------- Calculate Exoploration weight -------
- # Compute exploration weight based on trade off scheme
- explore_w, exploit_w = self.tradeoff_weights(tradeoff_scheme,
- old_EDX,
- old_EDY)
- print(f"\n Exploration weight={explore_w:0.3f} "
- f"Exploitation weight={exploit_w:0.3f}\n")
-
- # ------- EXPLOITATION: BayesOptDesign & ActiveLearning -------
- if explore_w != 1.0:
- # Check if all needed properties are set
- if not hasattr(self.ExpDesign, 'max_func_itr'):
- raise AttributeError('max_func_itr not given to the experimental design')
-
- # Create a sample pool for rejection sampling
- MCsize = 15000
- X_MC = self.ExpDesign.generate_samples(MCsize, 'random')
- candidates = self.ExpDesign.generate_samples(
- n_candidates, 'latin_hypercube')
-
- # Split the candidates in groups for multiprocessing
- split_cand = np.array_split(
- candidates, n_cand_groups, axis=0
- )
- # print(candidates)
- # print(split_cand)
- if self.parallel:
- results = Parallel(n_jobs=-1, backend='multiprocessing')(
- delayed(self.run_util_func)(
- exploit_method, split_cand[i], i, sigma2, var, X_MC)
- for i in range(n_cand_groups))
- else:
- results = []
- for i in range(n_cand_groups):
- results.append(self.run_util_func(exploit_method, split_cand[i], i, sigma2, var, X_MC))
-
- # Retrieve the results and append them
- U_J_d = np.concatenate([results[NofE][1] for NofE in
- range(n_cand_groups)])
-
- # Check if all scores are inf
- if np.isinf(U_J_d).all() or np.isnan(U_J_d).all():
- U_J_d = np.ones(len(U_J_d))
-
- # Get the expected value (mean) of the Utility score
- # for each cell
- if explore_method == 'Voronoi':
- U_J_d = np.mean(U_J_d.reshape(-1, n_candidates), axis=1)
-
- # Normalize U_J_d
- norm_U_J_d = U_J_d / np.sum(U_J_d)
- else:
- norm_U_J_d = np.zeros((len(scoreExploration)))
-
- # ------- Calculate Total score -------
- # ------- Trade off between EXPLORATION & EXPLOITATION -------
- # Accumulate the samples
- finalCandidates = np.concatenate((allCandidates, candidates), axis=0)
- finalCandidates = np.unique(finalCandidates, axis=0)
-
- # Calculations take into account both exploration and exploitation
- # samples without duplicates
- totalScore = np.zeros(finalCandidates.shape[0])
- # self.totalScore = totalScore
-
- for cand_idx in range(finalCandidates.shape[0]):
- # find candidate indices
- idx1 = np.where(allCandidates == finalCandidates[cand_idx])[0]
- idx2 = np.where(candidates == finalCandidates[cand_idx])[0]
-
- # exploration
- if idx1.shape[0] > 0:
- idx1 = idx1[0]
- totalScore[cand_idx] += explore_w * scoreExploration[idx1]
-
- # exploitation
- if idx2.shape[0] > 0:
- idx2 = idx2[0]
- totalScore[cand_idx] += exploit_w * norm_U_J_d[idx2]
-
- # Total score
- totalScore = exploit_w * norm_U_J_d
- totalScore += explore_w * scoreExploration
-
- # temp: Plot
- # dim = self.ExpDesign.X.shape[1]
- # if dim == 2:
- # plotter(self.ExpDesign.X, allCandidates, explore_method)
-
- # ------- Select the best candidate -------
- # find an optimal point subset to add to the initial design by
- # maximization of the utility score and taking care of NaN values
- temp = totalScore.copy()
- temp[np.isnan(totalScore)] = -np.inf
- sorted_idxtotalScore = np.argsort(temp)[::-1]
- bestIdx = sorted_idxtotalScore[:n_new_samples]
-
- # select the requested number of samples
- if explore_method == 'Voronoi':
- Xnew = np.zeros((n_new_samples, ndim))
- for i, idx in enumerate(bestIdx):
- X_can = explore.closestPoints[idx]
-
- # Calculate the maxmin score for the region of interest
- newSamples, maxminScore = explore.get_mc_samples(X_can)
-
- # select the requested number of samples
- Xnew[i] = newSamples[np.argmax(maxminScore)]
- else:
- # Changed this from allCandiates to full set of candidates
- # TODO: still not changed for e.g. 'Voronoi'
- Xnew = finalCandidates[sorted_idxtotalScore[:n_new_samples]]
-
-
- elif exploit_method.lower() == 'varoptdesign':
- # ------- EXPLOITATION: VarOptDesign -------
- UtilMethod = var
-
- # ------- Calculate Exoploration weight -------
- # Compute exploration weight based on trade off scheme
- explore_w, exploit_w = self.tradeoff_weights(tradeoff_scheme,
- old_EDX,
- old_EDY)
- print(f"\nweightExploration={explore_w:0.3f} "
- f"weightExploitation={exploit_w:0.3f}")
-
- # Generate candidate samples from Exploration class
- nMeasurement = old_EDY[OutputNames[0]].shape[1]
-
- # print(UtilMethod)
-
- # Find sensitive region
- if UtilMethod == 'LOOCV':
- LCerror = self.MetaModel.LCerror
- allModifiedLOO = np.zeros((len(old_EDX), len(OutputNames),
- nMeasurement))
- for y_idx, y_key in enumerate(OutputNames):
- for idx, key in enumerate(LCerror[y_key].keys()):
- allModifiedLOO[:, y_idx, idx] = abs(
- LCerror[y_key][key])
-
- ExploitScore = np.max(np.max(allModifiedLOO, axis=1), axis=1)
- # print(allModifiedLOO.shape)
-
- elif UtilMethod in ['EIGF', 'ALM']:
- # ----- All other in ['EIGF', 'ALM'] -----
- # Initilize the ExploitScore array
- # ExploitScore = np.zeros((len(old_EDX), len(OutputNames)))
-
- # Split the candidates in groups for multiprocessing
- if explore_method != 'Voronoi':
- split_cand = np.array_split(allCandidates,
- n_cand_groups,
- axis=0)
- goodSampleIdx = range(n_cand_groups)
- else:
- # Find indices of the Vornoi cells with samples
- goodSampleIdx = []
- for idx in range(len(explore.closest_points)):
- if len(explore.closest_points[idx]) != 0:
- goodSampleIdx.append(idx)
- split_cand = explore.closest_points
-
- # Split the candidates in groups for multiprocessing
- args = []
- for index in goodSampleIdx:
- args.append((exploit_method, split_cand[index], index,
- sigma2, var))
-
- # Multiprocessing
- pool = multiprocessing.Pool(multiprocessing.cpu_count())
- # With Pool.starmap_async()
- results = pool.starmap_async(self.run_util_func, args).get()
-
- # Close the pool
- pool.close()
-
- # Retrieve the results and append them
- if explore_method == 'Voronoi':
- ExploitScore = [np.mean(results[k][1]) for k in
- range(len(goodSampleIdx))]
- else:
- ExploitScore = np.concatenate(
- [results[k][1] for k in range(len(goodSampleIdx))])
-
- else:
- raise NameError('The requested utility function is not '
- 'available.')
-
- # print("ExploitScore:\n", ExploitScore)
-
- # find an optimal point subset to add to the initial design by
- # maximization of the utility score and taking care of NaN values
- # Total score
- # Normalize U_J_d
- ExploitScore = ExploitScore / np.sum(ExploitScore)
- totalScore = exploit_w * ExploitScore
- # print(totalScore.shape)
- # print(explore_w)
- # print(scoreExploration.shape)
- totalScore += explore_w * scoreExploration
-
- temp = totalScore.copy()
- sorted_idxtotalScore = np.argsort(temp, axis=0)[::-1]
- bestIdx = sorted_idxtotalScore[:n_new_samples]
-
- Xnew = np.zeros((n_new_samples, ndim))
- if explore_method != 'Voronoi':
- Xnew = allCandidates[bestIdx]
- else:
- for i, idx in enumerate(bestIdx.flatten()):
- X_can = explore.closest_points[idx]
- # plotter(self.ExpDesign.X, X_can, explore_method,
- # scoreExploration=None)
-
- # Calculate the maxmin score for the region of interest
- newSamples, maxminScore = explore.get_mc_samples(X_can)
-
- # select the requested number of samples
- Xnew[i] = newSamples[np.argmax(maxminScore)]
-
- elif exploit_method.lower() == 'alphabetic':
- # ------- EXPLOITATION: ALPHABETIC -------
- Xnew = self.util_AlphOptDesign(allCandidates, var)
-
- elif exploit_method == 'Space-filling':
- # ------- EXPLOITATION: SPACE-FILLING -------
- totalScore = scoreExploration
-
- # ------- Select the best candidate -------
- # find an optimal point subset to add to the initial design by
- # maximization of the utility score and taking care of NaN values
- temp = totalScore.copy()
- temp[np.isnan(totalScore)] = -np.inf
- sorted_idxtotalScore = np.argsort(temp)[::-1]
-
- # select the requested number of samples
- Xnew = allCandidates[sorted_idxtotalScore[:n_new_samples]]
-
- else:
- raise NameError('The requested design method is not available.')
-
- print("\n")
- print("\nRun No. {}:".format(old_EDX.shape[0] + 1))
- print("Xnew:\n", Xnew)
-
- # TODO: why does it also return None?
- return Xnew, None
-
- # -------------------------------------------------------------------------
- def util_AlphOptDesign(self, candidates, var='D-Opt'):
- """
- Enriches the Experimental design with the requested alphabetic
- criterion based on exploring the space with number of sampling points.
-
- Ref: Hadigol, M., & Doostan, A. (2018). Least squares polynomial chaos
- expansion: A review of sampling strategies., Computer Methods in
- Applied Mechanics and Engineering, 332, 382-407.
-
- Arguments
- ---------
- candidates : int?
- Number of candidate points to be searched
-
- var : string
- Alphabetic optimality criterion
-
- Returns
- -------
- X_new : array of shape (1, n_params)
- The new sampling location in the input space.
- """
- MetaModelOrig = self # TODO: this doesn't fully seem correct?
- n_new_samples = MetaModelOrig.ExpDesign.n_new_samples
- NCandidate = candidates.shape[0]
-
- # TODO: Loop over outputs
- OutputName = self.out_names[0]
-
- # To avoid changes ub original aPCE object
- # MetaModel = deepcopy(MetaModelOrig)
-
- # Old Experimental design
- oldExpDesignX = self.ExpDesign.X
-
- # TODO: Only one psi can be selected.
- # Suggestion: Go for the one with the highest LOO error
- # TODO: this is just a patch, need to look at again!
- Scores = list(self.MetaModel.score_dict['b_1'][OutputName].values())
- ModifiedLOO = [1 - score for score in Scores]
- outIdx = np.argmax(ModifiedLOO)
-
- # Initialize Phi to save the criterion's values
- Phi = np.zeros(NCandidate)
-
- # TODO: also patched here
- BasisIndices = self.MetaModel.basis_dict['b_1'][OutputName]["y_" + str(outIdx + 1)]
- P = len(BasisIndices)
-
- # ------ Old Psi ------------
- univ_p_val = self.MetaModel.univ_basis_vals(oldExpDesignX)
- Psi = create_psi(BasisIndices, univ_p_val)
-
- # ------ New candidates (Psi_c) ------------
- # Assemble Psi_c
- univ_p_val_c = self.MetaModel.univ_basis_vals(candidates)
- Psi_c = create_psi(BasisIndices, univ_p_val_c)
-
- for idx in range(NCandidate):
-
- # Include the new row to the original Psi
- Psi_cand = np.vstack((Psi, Psi_c[idx]))
-
- # Information matrix
- PsiTPsi = np.dot(Psi_cand.T, Psi_cand)
- M = PsiTPsi / (len(oldExpDesignX) + 1)
-
- if 1e-12 < np.linalg.cond(PsiTPsi) < 1 / sys.float_info.epsilon:
- # faster
- invM = linalg.solve(M, sparse.eye(PsiTPsi.shape[0]).toarray())
- else:
- # stabler
- invM = np.linalg.pinv(M)
-
- # ---------- Calculate optimality criterion ----------
- # Optimality criteria according to Section 4.5.1 in Ref.
-
- # D-Opt
- if var.lower() == 'd-opt':
- Phi[idx] = (np.linalg.det(invM)) ** (1 / P)
-
- # A-Opt
- elif var.lower() == 'a-opt':
- Phi[idx] = np.trace(invM)
-
- # K-Opt
- elif var.lower() == 'k-opt':
- Phi[idx] = np.linalg.cond(M)
-
- else:
- # print(var.lower())
- raise Exception('The optimality criterion you requested has '
- 'not been implemented yet!')
-
- # find an optimal point subset to add to the initial design
- # by minimization of the Phi
- sorted_idxtotalScore = np.argsort(Phi)
-
- # select the requested number of samples
- Xnew = candidates[sorted_idxtotalScore[:n_new_samples]]
-
- return Xnew
-
# -------------------------------------------------------------------------
def _normpdf(self, y_hat_pce, std_pce, obs_data, total_sigma2s,
rmse=None):
@@ -1883,7 +634,6 @@ class Engine:
for idx, out in enumerate(self.out_names):
# (Meta)Model Output
- # print(y_hat_pce[out])
nsamples, nout = y_hat_pce[out].shape
# Prepare data and remove NaN
diff --git a/src/bayesvalidrox/surrogate_models/exp_designs.py b/src/bayesvalidrox/surrogate_models/exp_designs.py
index 7ec80a321d3ed948af73e0b19d511b39301f2686..f4c29528613e90d6574e81535ea6da346624571f 100644
--- a/src/bayesvalidrox/surrogate_models/exp_designs.py
+++ b/src/bayesvalidrox/surrogate_models/exp_designs.py
@@ -247,7 +247,6 @@ class ExpDesigns(InputSpace):
samples = None
sampling_method = self.sampling_method
# Pass user-defined samples as ED
- print(sampling_method)
if sampling_method == 'user':
if self.X is None:
raise AttributeError('User-defined sampling cannot proceed as no samples provided. Please add them to '
@@ -467,7 +466,6 @@ class ExpDesigns(InputSpace):
-------
"""
- print(raw_data[parIdx])
return apoly_construction(self.raw_data[parIdx], max_deg)
for i in range(self.ndim):
diff --git a/src/bayesvalidrox/surrogate_models/sequential_design.py b/src/bayesvalidrox/surrogate_models/sequential_design.py
new file mode 100644
index 0000000000000000000000000000000000000000..d4004b8b8c60ce4ffa957f4855d462566630f8f5
--- /dev/null
+++ b/src/bayesvalidrox/surrogate_models/sequential_design.py
@@ -0,0 +1,1750 @@
+# -*- coding: utf-8 -*-
+"""
+Engine to train the surrogate
+
+"""
+from copy import deepcopy, copy
+import joblib
+from joblib import Parallel, delayed
+import matplotlib.pyplot as plt
+import multiprocessing
+import numpy as np
+import os
+import pandas as pd
+import pathlib
+import scipy.optimize as opt
+from scipy import stats, signal, linalg, sparse
+from scipy.spatial import distance
+from sklearn.metrics import mean_squared_error
+import seaborn as sns
+import sys
+from tqdm import tqdm
+
+from bayesvalidrox.bayes_inference.bayes_inference import BayesInference
+from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
+from .exploration import Exploration
+from .surrogate_models import create_psi
+
+def hellinger_distance(P, Q):
+ """
+ Hellinger distance between two continuous distributions.
+
+ The maximum distance 1 is achieved when P assigns probability zero to
+ every set to which Q assigns a positive probability, and vice versa.
+ 0 (identical) and 1 (maximally different)
+
+ Parameters
+ ----------
+ P : array
+ Reference likelihood.
+ Q : array
+ Estimated likelihood.
+
+ Returns
+ -------
+ float
+ Hellinger distance of two distributions.
+
+ """
+ P = np.array(P)
+ Q = np.array(Q)
+
+ mu1 = P.mean()
+ Sigma1 = np.std(P)
+
+ mu2 = Q.mean()
+ Sigma2 = np.std(Q)
+
+ term1 = np.sqrt(2 * Sigma1 * Sigma2 / (Sigma1 ** 2 + Sigma2 ** 2))
+
+ term2 = np.exp(-.25 * (mu1 - mu2) ** 2 / (Sigma1 ** 2 + Sigma2 ** 2))
+
+ H_squared = 1 - term1 * term2
+
+ return np.sqrt(H_squared)
+
+
+def logpdf(x, mean, cov):
+ """
+ Computes the likelihood based on a multivariate normal distribution.
+
+ Parameters
+ ----------
+ x : TYPE
+ DESCRIPTION.
+ mean : array_like
+ Observation data.
+ cov : 2d array
+ Covariance matrix of the distribution.
+
+ Returns
+ -------
+ log_lik : float
+ Log likelihood.
+
+ """
+ n = len(mean)
+ L = linalg.cholesky(cov, lower=True)
+ beta = np.sum(np.log(np.diag(L)))
+ dev = x - mean
+ alpha = dev.dot(linalg.cho_solve((L, True), dev))
+ log_lik = -0.5 * alpha - beta - n / 2. * np.log(2 * np.pi)
+
+ return log_lik
+
+
+def subdomain(Bounds, n_new_samples):
+ """
+ Divides a domain defined by Bounds into subdomains.
+
+ Parameters
+ ----------
+ Bounds : list of tuples
+ List of lower and upper bounds.
+ n_new_samples : int
+ Number of samples to divide the domain for.
+
+ Returns
+ -------
+ Subdomains : List of tuples of tuples
+ Each tuple of tuples divides one set of bounds into n_new_samples parts.
+
+ """
+ n_params = len(Bounds)
+ n_subdomains = n_new_samples + 1
+ LinSpace = np.zeros((n_params, n_subdomains))
+
+ for i in range(n_params):
+ LinSpace[i] = np.linspace(start=Bounds[i][0], stop=Bounds[i][1],
+ num=n_subdomains)
+ Subdomains = []
+ for k in range(n_subdomains - 1):
+ mylist = []
+ for i in range(n_params):
+ mylist.append((LinSpace[i, k + 0], LinSpace[i, k + 1]))
+ Subdomains.append(tuple(mylist))
+
+ return Subdomains
+
+
+class SequentialDesign:
+ """
+ Contains options for choosing the next training sample iteratively.
+
+ """
+
+ def __init__(self, MetaMod, Model, ExpDes, engine, parallel=False):
+ self.MetaModel = MetaMod # Surrogate should be trained
+ self.Model = Model
+ self.ExpDesign = ExpDes
+ self.parallel = parallel
+ self.engine = engine
+
+ # Init other parameters
+ self._y_hat_prev = None
+
+ def start_seqdesign(self) -> None:
+ """
+ Do all the preparations that need to be run before the actual training
+
+ Returns
+ -------
+ None
+
+ """
+ None
+
+
+ # -------------------------------------------------------------------------
+ def choose_next_sample(self, sigma2=None, n_candidates=5, var='DKL'):
+ """
+ Runs optimal sequential design.
+
+ Parameters
+ ----------
+ sigma2 : dict, optional
+ A dictionary containing the measurement errors (sigma^2). The
+ default is None.
+ n_candidates : int, optional
+ Number of candidate samples. The default is 5.
+ var : string, optional
+ Utility function. The default is None. # TODO: default is set to DKL, not none
+
+ Raises
+ ------
+ NameError
+ Wrong utility function.
+
+ Returns
+ -------
+ Xnew : array (n_samples, n_params)
+ Selected new training point(s).
+ """
+
+ # Initialization
+ Bounds = self.ExpDesign.bound_tuples
+ n_new_samples = self.ExpDesign.n_new_samples
+ explore_method = self.ExpDesign.explore_method
+ exploit_method = self.ExpDesign.exploit_method
+ n_cand_groups = self.ExpDesign.n_cand_groups
+ tradeoff_scheme = self.ExpDesign.tradeoff_scheme
+
+ old_EDX = self.ExpDesign.X
+ old_EDY = self.ExpDesign.Y.copy()
+ ndim = self.ExpDesign.X.shape[1]
+ OutputNames = self.out_names
+
+ # -----------------------------------------
+ # ----------- CUSTOMIZED METHODS ----------
+ # -----------------------------------------
+ # Utility function exploit_method provided by user
+ if exploit_method.lower() == 'user':
+ # TODO: is the exploit_method meant here?
+ if not hasattr(self.ExpDesign, 'ExploitFunction') or self.ExpDesign.ExploitFunction is None:
+ raise AttributeError(
+ 'Function `ExploitFunction` not given to the ExpDesign, thus cannor run user-defined sequential'
+ 'scheme')
+ # TODO: syntax does not fully match the rest - can test this??
+ Xnew, filteredSamples = self.ExpDesign.ExploitFunction(self)
+
+ print("\n")
+ print("\nXnew:\n", Xnew)
+
+ return Xnew, filteredSamples
+
+ # Dual-Annealing works differently from the rest, so deal with this first
+ # Here exploration and exploitation are performed simulataneously
+ if explore_method.lower() == 'dual annealing':
+ # ------- EXPLORATION: OPTIMIZATION -------
+ import time
+ start_time = time.time()
+
+ # Divide the domain to subdomains
+ subdomains = subdomain(Bounds, n_new_samples)
+
+ # Multiprocessing
+ if self.parallel:
+ args = []
+ for i in range(n_new_samples):
+ args.append((exploit_method, subdomains[i], sigma2, var, i))
+ pool = multiprocessing.Pool(multiprocessing.cpu_count())
+
+ # With Pool.starmap_async()
+ results = pool.starmap_async(self.dual_annealing, args).get()
+
+ # Close the pool
+ pool.close()
+ # Without multiprocessing
+ else:
+ results = []
+ for i in range(n_new_samples):
+ results.append(self.dual_annealing(exploit_method, subdomains[i], sigma2, var, i))
+
+ # New sample
+ Xnew = np.array([results[i][1] for i in range(n_new_samples)])
+ print("\nXnew:\n", Xnew)
+
+ # Computational cost
+ elapsed_time = time.time() - start_time
+ print("\n")
+ print(f"Elapsed_time: {round(elapsed_time, 2)} sec.")
+ print('-' * 20)
+
+ return Xnew, None
+
+ # ------- Calculate Exploration weight -------
+ # Compute exploration weight based on trade off scheme
+ explore_w, exploit_w = self.tradeoff_weights(tradeoff_scheme,
+ old_EDX,
+ old_EDY)
+ print(f"\n Exploration weight={explore_w:0.3f} "
+ f"Exploitation weight={exploit_w:0.3f}\n")
+
+ # Generate the candidate samples
+ # TODO: here use the sampling method provided by the expdesign?
+ # sampling_method = self.ExpDesign.sampling_method
+
+ # TODO: changed this from 'random' for LOOCV
+ # TODO: these are commented out as they are not used !?
+ # if explore_method == 'LOOCV':
+ # allCandidates = self.ExpDesign.generate_samples(n_candidates,
+ # sampling_method)
+ # else:
+ # allCandidates, scoreExploration = explore.get_exploration_samples()
+
+ # -----------------------------------------
+ # ---------- EXPLORATION METHODS ----------
+ # -----------------------------------------
+ # ToDo: Move this if/else into its own function called "do_exploration", which should select the
+ # exploration samples, and assign exploration scores. We should send it explore_score, for if/else stmts
+ # ToDo: Check if explore_scores can be nan, and remove them from any score normalization
+ if explore_method.lower() == 'voronoi':
+ raise AttributeError('Exploration with voronoi currently not supported!')
+ #print('WARNING: Exploration with Voronoi ')
+ if explore_method.lower() == 'loocv':
+ # -----------------------------------------------------------------
+ # TODO: LOOCV model construnction based on Feng et al. (2020)
+ # 'LOOCV':
+ # Initilize the ExploitScore array
+
+ # Generate random samples
+ allCandidates = self.ExpDesign.generate_samples(n_candidates,
+ 'random')
+
+ # Construct error model based on LCerror
+ errorModel = self.MetaModel.create_ModelError(old_EDX, self.LCerror)
+ self.errorModel.append(copy(errorModel))
+
+ # Evaluate the error models for allCandidates
+ eLCAllCands, _ = errorModel.eval_errormodel(allCandidates)
+ # Select the maximum as the representative error
+ eLCAllCands = np.dstack(eLCAllCands.values())
+ eLCAllCandidates = np.max(eLCAllCands, axis=1)[:, 0]
+
+ # Normalize the error w.r.t the maximum error
+ scoreExploration = eLCAllCandidates / np.sum(eLCAllCandidates)
+
+ else:
+ # ------- EXPLORATION: SPACE-FILLING DESIGN -------
+ # ToDo: Remove Exploration class and merge the functions into SequentialDesign class
+ # Generate candidate samples from Exploration class
+ explore = Exploration(self.ExpDesign, n_candidates)
+ explore.w = 100 # * ndim #500 # TODO: where does this value come from?
+ # Select criterion (mc-intersite-proj-th, mc-intersite-proj)
+ explore.mc_criterion = 'mc-intersite-proj'
+ allCandidates, scoreExploration = explore.get_exploration_samples()
+
+ # Temp: ---- Plot all candidates -----
+ # ToDo: Make its own function, called inside of the select_exploration_samples function.
+ if ndim == 2:
+ def plotter(points, allCandidates, Method,
+ scoreExploration=None):
+ """
+ unknown
+
+ Parameters
+ ----------
+ points
+ allCandidates
+ Method
+ scoreExploration
+
+ Returns
+ -------
+
+ """
+ if Method.lower() == 'voronoi':
+ from scipy.spatial import Voronoi, voronoi_plot_2d
+ vor = Voronoi(points)
+ fig = voronoi_plot_2d(vor)
+ ax1 = fig.axes[0]
+ else:
+ fig = plt.figure()
+ ax1 = fig.add_subplot(111)
+ ax1.scatter(points[:, 0], points[:, 1], s=10, c='r',
+ marker="s", label='Old Design Points')
+ ax1.scatter(allCandidates[:, 0], allCandidates[:, 1], s=10,
+ c='b', marker="o", label='Design candidates')
+ for i in range(points.shape[0]):
+ txt = 'p' + str(i + 1)
+ ax1.annotate(txt, (points[i, 0], points[i, 1]))
+ if scoreExploration is not None:
+ for i in range(allCandidates.shape[0]):
+ txt = str(round(scoreExploration[i], 5))
+ ax1.annotate(txt, (allCandidates[i, 0],
+ allCandidates[i, 1]))
+
+ plt.xlim(self.bound_tuples[0])
+ plt.ylim(self.bound_tuples[1])
+ # plt.show()
+ plt.legend(loc='upper left')
+
+ # -----------------------------------------
+ # --------- EXPLOITATION METHODS ----------
+ # -----------------------------------------
+ if exploit_method.lower() == 'bayesoptdesign' or \
+ exploit_method.lower() == 'bayesactdesign':
+
+ # ------- EXPLOITATION: BayesOptDesign & ActiveLearning -------
+ if explore_w != 1.0:
+ # Check if all needed properties are set
+ if not hasattr(self.ExpDesign, 'max_func_itr'):
+ raise AttributeError('max_func_itr not given to the experimental design')
+
+
+ # Create a sample pool for rejection sampling
+ # ToDo: remove from here, add only to BayesOptDesign option
+ MCsize = 15000
+ X_MC = self.ExpDesign.generate_samples(MCsize, 'random')
+
+ # Split the candidates in groups for multiprocessing
+ split_cand = np.array_split(
+ allCandidates, n_cand_groups, axis=0
+ )
+ if self.parallel:
+ results = Parallel(n_jobs=-1, backend='multiprocessing')(
+ delayed(self.run_util_func)(
+ exploit_method, split_cand[i], i, sigma2, var, X_MC)
+ for i in range(n_cand_groups))
+ else:
+ results = []
+ for i in range(n_cand_groups):
+ results.append(self.run_util_func(exploit_method, split_cand[i], i, sigma2, var, X_MC))
+
+ # Retrieve the results and append them
+ # ToDo: Rename U_J_D (here and everyhwere) to something more representative
+ self.results = results
+ U_J_d = np.concatenate([results[NofE][1] for NofE in
+ range(n_cand_groups)])
+
+ # Check if all scores are inf
+ if np.isinf(U_J_d).all() or np.isnan(U_J_d).all():
+ U_J_d = np.ones(len(U_J_d))
+
+ # Get the expected value (mean) of the Utility score
+ # for each cell
+ if explore_method.lower() == 'voronoi':
+ U_J_d = np.mean(U_J_d.reshape(-1, n_candidates), axis=1)
+
+ # Normalize U_J_d
+ # norm_U_J_D = U_J_d / np.nansum(np.abs(U_J_d)) # Possible solution
+ norm_scoreExploitation = U_J_d / np.sum(U_J_d)
+
+ else:
+ norm_scoreExploitation = np.zeros((len(scoreExploration)))
+
+ # temp: Plot
+ # dim = self.ExpDesign.X.shape[1]
+ # if dim == 2:
+ # plotter(self.ExpDesign.X, allCandidates, explore_method)
+ opt_type = 'maximization'
+
+ elif exploit_method.lower() == 'varoptdesign':
+ # ------- EXPLOITATION: VarOptDesign -------
+ UtilMethod = var
+
+ # ------- Calculate Exoploration weight -------
+ # Compute exploration weight based on trade off scheme
+ explore_w, exploit_w = self.tradeoff_weights(tradeoff_scheme,
+ old_EDX,
+ old_EDY)
+ print(f"\nweightExploration={explore_w:0.3f} "
+ f"weightExploitation={exploit_w:0.3f}")
+
+ # Generate candidate samples from Exploration class
+ nMeasurement = old_EDY[OutputNames[0]].shape[1]
+
+ # Find sensitive region
+ if UtilMethod.lower() == 'loocv':
+ # TODO: why is this not inside the VarOptDesign function?
+ LCerror = self.MetaModel.LCerror
+ allModifiedLOO = np.zeros((len(old_EDX), len(OutputNames),
+ nMeasurement))
+ for y_idx, y_key in enumerate(OutputNames):
+ for idx, key in enumerate(LCerror[y_key].keys()):
+ allModifiedLOO[:, y_idx, idx] = abs(
+ LCerror[y_key][key])
+
+ ExploitScore = np.max(np.max(allModifiedLOO, axis=1), axis=1)
+
+ elif UtilMethod in ['EIGF', 'ALM']:
+ # ToDo: Check the methods it actually can receive (ALC is missing from conditional list and code)
+ # ----- All other in ['EIGF', 'ALM'] -----
+
+ # Split the candidates in groups for multiprocessing
+ if explore_method.lower() != 'voronoi':
+ split_cand = np.array_split(allCandidates,
+ n_cand_groups,
+ axis=0)
+ goodSampleIdx = range(n_cand_groups)
+ else:
+ # Find indices of the Vornoi cells with samples
+ goodSampleIdx = []
+ for idx in range(len(explore.closest_points)):
+ if len(explore.closest_points[idx]) != 0:
+ goodSampleIdx.append(idx)
+ split_cand = explore.closest_points
+
+ # Split the candidates in groups for multiprocessing
+ args = []
+ for index in goodSampleIdx:
+ args.append((exploit_method, split_cand[index], index,
+ sigma2, var))
+
+ # Multiprocessing
+ pool = multiprocessing.Pool(multiprocessing.cpu_count())
+ # With Pool.starmap_async()
+ results = pool.starmap_async(self.run_util_func, args).get()
+
+ # Close the pool
+ pool.close()
+
+ # Retrieve the results and append them
+ if explore_method.lower() == 'voronoi':
+ ExploitScore = [np.mean(results[k][1]) for k in
+ range(len(goodSampleIdx))]
+ else:
+ ExploitScore = np.concatenate(
+ [results[k][1] for k in range(len(goodSampleIdx))])
+
+ else:
+ raise NameError('The requested utility function is not '
+ 'available.')
+
+ # Total score - Normalize U_J_d
+ norm_scoreExploitation = ExploitScore / np.sum(ExploitScore)
+ opt_type = 'maximization'
+
+ elif exploit_method.lower() == 'alphabetic':
+ # ToDo: Check function to see what it does for scores/how it chooses points, so it gives as an output the
+ # scores. See how it works with exploration_scores.
+ # TODO: Rethink the final accumulation of scores for this function
+ # Should this be reworked to maximization as well?
+ # ------- EXPLOITATION: ALPHABETIC -------
+ norm_scoreExploitation = self.util_AlphOptDesign(allCandidates, var)
+ opt_type = 'minimization'
+
+ elif exploit_method.lower() == 'space-filling':
+ # ------- EXPLOITATION: SPACE-FILLING -------
+ norm_scoreExploitation = scoreExploration
+ exploit_w = 0
+ opt_type = 'maximization'
+
+ else:
+ raise NameError('The requested design method is not available.')
+
+ # Accumulate all candidates and scores
+ # TODO: recheck if this line holds true for all combinations of methods
+ # TODO: for the combination none, voronoi, BOD+MI the exploration scores contain 10*more values than the exploitation scores
+ # This seems to be an issue resulting from the voronoi sampling, not BODMI
+ #print('Shapes of components of the weights')
+ #print(f'Exploration: {explore_w} * {scoreExploration.shape}')
+ #print(f'Exploitation: {exploit_w} * {norm_scoreExploitation.shape}')
+ finalCandidates = allCandidates
+ totalScore = exploit_w * norm_scoreExploitation + explore_w * scoreExploration
+
+ # Choose the new training samples
+ # If the total weights should be maximized
+ if opt_type == 'maximization':
+
+ # ------- Select the best candidate -------
+ # find an optimal point subset to add to the initial design by
+ # maximization of the utility score and taking care of NaN values
+ temp = totalScore.copy()
+ temp[np.isnan(totalScore)] = -np.inf # Since we are maximizing
+ sorted_idxtotalScore = np.argsort(temp)[::-1]
+ print(sorted_idxtotalScore)
+ print(n_new_samples)
+ bestIdx = sorted_idxtotalScore[:n_new_samples]
+ if type(bestIdx) is int:
+ bestIdx = [bestIdx]
+
+ # select the requested number of samples
+ if explore_method.lower() == 'voronoi':
+ Xnew = np.zeros((n_new_samples, ndim))
+ for i, idx in enumerate(bestIdx):
+ print(explore.closestPoints)
+ X_can = explore.closestPoints[idx]
+
+ # Calculate the maxmin score for the region of interest
+ newSamples, maxminScore = explore.get_mc_samples(X_can) # TODO: Understand this line!
+
+ # select the requested number of samples
+ Xnew[i] = newSamples[np.argmax(maxminScore)]
+ else:
+ # Changed this from allCandiates to full set of candidates
+ # TODO: still not changed for e.g. 'Voronoi'
+ Xnew = finalCandidates[sorted_idxtotalScore[:n_new_samples]]
+
+ # If the total weights should be maximized
+ elif opt_type == 'minimization':
+ # find an optimal point subset to add to the initial design
+ # by minimization of the Phi
+ sorted_idxtotalScore = np.argsort(totalScore)
+
+ # select the requested number of samples
+ Xnew = finalCandidates[sorted_idxtotalScore[:n_new_samples]]
+
+
+ print("\n")
+ print("\nRun No. {}:".format(old_EDX.shape[0] + 1))
+ print("Xnew:\n", Xnew)
+
+ # TODO: why does it also return None?
+ return Xnew, None
+
+ # -------------------------------------------------------------------------
+ def tradeoff_weights(self, tradeoff_scheme, old_EDX, old_EDY):
+ """
+ Calculates weights for exploration scores based on the requested
+ scheme: `None`, `equal`, `epsilon-decreasing` and `adaptive`.
+
+ `None`: No exploration.
+ `equal`: Same weights for exploration and exploitation scores.
+ `epsilon-decreasing`: Start with more exploration and increase the
+ influence of exploitation along the way with an exponential decay
+ function
+ `adaptive`: An adaptive method based on:
+ Liu, Haitao, Jianfei Cai, and Yew-Soon Ong. "An adaptive sampling
+ approach for Kriging metamodeling by maximizing expected prediction
+ error." Computers & Chemical Engineering 106 (2017): 171-182.
+
+ Parameters
+ ----------
+ tradeoff_scheme : string
+ Trade-off scheme for exloration and exploitation scores.
+ old_EDX : array (n_samples, n_params)
+ Old experimental design (training points).
+ old_EDY : dict
+ Old model responses (targets).
+
+ Returns
+ -------
+ exploration_weight : float
+ Exploration weight.
+ exploitation_weight: float
+ Exploitation weight.
+
+ """
+ exploration_weight = None
+
+ if tradeoff_scheme is None:
+ exploration_weight = 0
+
+ elif tradeoff_scheme.lower() == 'equal':
+ exploration_weight = 0.5
+
+ elif tradeoff_scheme.lower() == 'epsilon-decreasing':
+ # epsilon-decreasing scheme
+ # Start with more exploration and increase the influence of
+ # exploitation along the way with an exponential decay function
+ initNSamples = self.ExpDesign.n_init_samples
+ n_max_samples = self.ExpDesign.n_max_samples
+
+ itrNumber = (self.ExpDesign.X.shape[0] - initNSamples)
+ itrNumber //= self.ExpDesign.n_new_samples
+
+ tau2 = -(n_max_samples - initNSamples - 1) / np.log(1e-8)
+ exploration_weight = signal.windows.exponential(n_max_samples - initNSamples,
+ 0, tau2, False)[itrNumber]
+
+ elif tradeoff_scheme.lower() == 'adaptive':
+
+ # Extract itrNumber
+ initNSamples = self.ExpDesign.n_init_samples
+ # n_max_samples = self.ExpDesign.n_max_samples
+ itrNumber = (self.ExpDesign.X.shape[0] - initNSamples)
+ itrNumber //= self.ExpDesign.n_new_samples
+
+ if itrNumber == 0:
+ exploration_weight = 0.5
+ else:
+ # New adaptive trade-off according to Liu et al. (2017)
+ # Mean squared error for last design point
+ last_EDX = old_EDX[-1].reshape(1, -1)
+ lastPCEY, _ = self.MetaModel.eval_metamodel(samples=last_EDX)
+ pce_y = np.array(list(lastPCEY.values()))[:, 0]
+ y = np.array(list(old_EDY.values()))[:, -1, :]
+ mseError = mean_squared_error(pce_y, y)
+
+ # Mean squared CV - error for last design point
+ pce_y_prev = np.array(list(self._y_hat_prev.values()))[:, 0]
+ mseCVError = mean_squared_error(pce_y_prev, y)
+
+ exploration_weight = min([0.5 * mseError / mseCVError, 1])
+
+ # Exploitation weight
+ exploitation_weight = 1 - exploration_weight
+
+ return exploration_weight, exploitation_weight
+
+ # -------------------------------------------------------------------------
+ def run_util_func(self, method, candidates, index, sigma2Dict=None,
+ var=None, X_MC=None):
+ """
+ Runs the utility function based on the given method.
+
+ Parameters
+ ----------
+ method : string
+ Exploitation method: `VarOptDesign`, `BayesActDesign` and
+ `BayesOptDesign`.
+ candidates : array of shape (n_samples, n_params)
+ All candidate parameter sets.
+ index : int
+ ExpDesign index.
+ sigma2Dict : dict, optional
+ A dictionary containing the measurement errors (sigma^2). The
+ default is None.
+ var : string, optional
+ Utility function. The default is None.
+ X_MC : TYPE, optional
+ DESCRIPTION. The default is None.
+
+ Returns
+ -------
+ index : TYPE
+ DESCRIPTION.
+ List
+ Scores.
+
+ """
+
+ if method.lower() == 'varoptdesign':
+ # U_J_d = self.util_VarBasedDesign(candidates, index, var)
+ U_J_d = np.zeros((candidates.shape[0]))
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="varoptdesign"):
+ U_J_d[idx] = self.util_VarBasedDesign(X_can, index, var)
+
+ elif method.lower() == 'bayesactdesign':
+ NCandidate = candidates.shape[0]
+ U_J_d = np.zeros(NCandidate)
+ # Evaluate all candidates
+ y_can, std_can = self.MetaModel.eval_metamodel(samples=candidates)
+ # loop through candidates
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="BAL Design"):
+ y_hat = {key: items[idx] for key, items in y_can.items()}
+ std = {key: items[idx] for key, items in std_can.items()}
+
+ # print(y_hat)
+ # print(std)
+ U_J_d[idx] = self.util_BayesianActiveDesign(
+ y_hat, std, sigma2Dict, var)
+
+ elif method.lower() == 'bayesoptdesign':
+ # ToDo: Create X_MC here, since it is not used in the other active learning approaches.
+ NCandidate = candidates.shape[0]
+ U_J_d = np.zeros(NCandidate)
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="OptBayesianDesign"):
+ U_J_d[idx] = self.util_BayesianDesign(X_can, X_MC, sigma2Dict,
+ var)
+ return index, -1 * U_J_d
+
+
+ # -------------------------------------------------------------------------
+ def util_VarBasedDesign(self, X_can, index, util_func='Entropy'):
+ """
+ Computes the exploitation scores based on:
+ active learning MacKay(ALM) and active learning Cohn (ALC)
+ Paper: Sequential Design with Mutual Information for Computer
+ Experiments (MICE): Emulation of a Tsunami Model by Beck and Guillas
+ (2016)
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ index : int
+ Model output index.
+ util_func : string, optional
+ Exploitation utility function. The default is 'Entropy'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+ MetaModel = self.MetaModel
+ ED_X = self.ExpDesign.X
+ out_dict_y = self.ExpDesign.Y
+ out_names = self.out_names
+
+ # Run the Metamodel for the candidate
+ X_can = X_can.reshape(1, -1)
+ Y_PC_can, std_PC_can = MetaModel.eval_metamodel(samples=X_can)
+
+ score = None
+ if util_func.lower() == 'alm':
+ # ----- Entropy/MMSE/active learning MacKay(ALM) -----
+ # Compute perdiction variance of the old model
+ canPredVar = {key: std_PC_can[key] ** 2 for key in out_names}
+
+ varPCE = np.zeros((len(out_names), X_can.shape[0]))
+ for KeyIdx, key in enumerate(out_names):
+ varPCE[KeyIdx] = np.max(canPredVar[key], axis=1)
+ score = np.max(varPCE, axis=0)
+
+ elif util_func.lower() == 'eigf':
+ # ----- Expected Improvement for Global fit -----
+ # Find closest EDX to the candidate
+ distances = distance.cdist(ED_X, X_can, 'euclidean')
+ index = np.argmin(distances)
+
+ # Compute perdiction error and variance of the old model
+ predError = {key: Y_PC_can[key] for key in out_names}
+ canPredVar = {key: std_PC_can[key] ** 2 for key in out_names}
+
+ # Compute perdiction error and variance of the old model
+ # Eq (5) from Liu et al.(2018)
+ EIGF_PCE = np.zeros((len(out_names), X_can.shape[0]))
+ for KeyIdx, key in enumerate(out_names):
+ residual = predError[key] - out_dict_y[key][int(index)]
+ var = canPredVar[key]
+ EIGF_PCE[KeyIdx] = np.max(residual ** 2 + var, axis=1)
+ score = np.max(EIGF_PCE, axis=0)
+
+ return -1 * score # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def util_BayesianActiveDesign(self, y_hat, std, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian active design criterion (var).
+
+ It is based on the following paper:
+ Oladyshkin, Sergey, Farid Mohammadi, Ilja Kroeker, and Wolfgang Nowak.
+ "Bayesian3 active learning for the gaussian process emulator using
+ information theory." Entropy 22, no. 8 (2020): 890.
+
+ Parameters
+ ----------
+ y_hat : unknown
+ std : unknown
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ BAL design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # Get the data
+ obs_data = self.Model.observations
+ # TODO: this should be optimizable to be calculated explicitly
+ if hasattr(self.Model, 'n_obs'):
+ n_obs = self.Model.n_obs
+ else:
+ n_obs = self.n_obs
+ mc_size = 10000
+
+ # Sample a distribution for a normal dist
+ # with Y_mean_can as the mean and Y_std_can as std.
+ Y_MC, std_MC = {}, {}
+ logPriorLikelihoods = np.zeros(mc_size)
+ for key in list(y_hat):
+ cov = np.diag(std[key] ** 2)
+ print(key, y_hat[key], std[key])
+ # TODO: added the allow_singular = True here
+ rv = stats.multivariate_normal(mean=y_hat[key], cov=cov, allow_singular=True)
+ Y_MC[key] = rv.rvs(size=mc_size)
+ logPriorLikelihoods += rv.logpdf(Y_MC[key])
+ std_MC[key] = np.zeros((mc_size, y_hat[key].shape[0]))
+
+ # Likelihood computation (Comparison of data and simulation
+ # results via PCE with candidate design)
+ likelihoods = self._normpdf(Y_MC, std_MC, obs_data, sigma2Dict)
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, mc_size)[0]
+
+ # Reject the poorly performed prior
+ accepted = (likelihoods / np.max(likelihoods)) >= unif
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods), dtype=np.longdouble) # float128)
+
+ # Posterior-based expectation of likelihoods
+ postLikelihoods = likelihoods[accepted]
+ postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Posterior-based expectation of prior densities
+ postExpPrior = np.mean(logPriorLikelihoods[accepted])
+
+ # Utility function Eq.2 in Ref. (2)
+ # Posterior covariance matrix after observing data y
+ # Kullback-Leibler Divergence (Sergey's paper)
+ U_J_d = None
+ if var.lower() == 'dkl':
+
+ # TODO: Calculate the correction factor for BME
+ # BMECorrFactor = self.BME_Corr_Weight(PCE_SparseBayes_can,
+ # ObservationData, sigma2Dict)
+ # BME += BMECorrFactor
+ # Haun et al implementation
+ # U_J_d = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
+ U_J_d = postExpLikelihoods - logBME
+
+ # Marginal log likelihood
+ elif var.lower() == 'bme':
+ U_J_d = np.nanmean(likelihoods)
+
+ # Entropy-based information gain
+ elif var.lower() == 'infentropy':
+ logBME = np.log(np.nanmean(likelihoods))
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
+ U_J_d = infEntropy * -1 # -1 for minimization
+
+ # Bayesian information criterion
+ elif var.lower() == 'bic':
+ coeffs = self.MetaModel.coeffs_dict.values()
+ nModelParams = max(len(v) for val in coeffs for v in val.values())
+ maxL = np.nanmax(likelihoods)
+ U_J_d = -2 * np.log(maxL) + np.log(n_obs) * nModelParams
+
+ # Akaike information criterion
+ elif var.lower() == 'aic':
+ coeffs = self.MetaModel.coeffs_dict.values()
+ nModelParams = max(len(v) for val in coeffs for v in val.values())
+ maxlogL = np.log(np.nanmax(likelihoods))
+ AIC = -2 * maxlogL + 2 * nModelParams
+ # 2 * nModelParams * (nModelParams+1) / (n_obs-nModelParams-1)
+ penTerm = 0
+ U_J_d = 1 * (AIC + penTerm)
+
+ # Deviance information criterion
+ elif var.lower() == 'dic':
+ # D_theta_bar = np.mean(-2 * Likelihoods)
+ N_star_p = 0.5 * np.var(np.log(likelihoods[likelihoods != 0]))
+ Likelihoods_theta_mean = self._normpdf(
+ y_hat, std, obs_data, sigma2Dict
+ )
+ DIC = -2 * np.log(Likelihoods_theta_mean) + 2 * N_star_p
+
+ U_J_d = DIC
+
+ else:
+ print('The algorithm you requested has not been implemented yet!')
+
+ # Handle inf and NaN (replace by zero)
+ if np.isnan(U_J_d) or U_J_d == -np.inf or U_J_d == np.inf:
+ U_J_d = 0.0
+
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+
+ return -1 * U_J_d # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def util_BayesianDesign(self, X_can, X_MC, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian sequential design criterion (var).
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ X_MC : unknown
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ Bayesian design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # To avoid changes ub original aPCE object
+ MetaModel = self.MetaModel
+ out_names = self.out_names
+ if X_can.ndim == 1:
+ X_can = X_can.reshape(1, -1)
+
+ # Compute the mean and std based on the MetaModel
+ # pce_means, pce_stds = self._compute_pce_moments(MetaModel)
+ if var.lower() == 'alc':
+ Y_MC, Y_MC_std = MetaModel.eval_metamodel(samples=X_MC)
+
+ # Old Experimental design
+ oldExpDesignX = self.ExpDesign.X
+ oldExpDesignY = self.ExpDesign.Y
+
+ # Evaluate the PCE metamodels at that location ???
+ Y_PC_can, Y_std_can = MetaModel.eval_metamodel(samples=X_can)
+ PCE_Model_can = deepcopy(MetaModel)
+ # TODO: this is really not clean, create a workaround for this issue!
+ engine_can = deepcopy(self.engine)
+ # Add the candidate to the ExpDesign
+ NewExpDesignX = np.vstack((oldExpDesignX, X_can))
+
+ NewExpDesignY = {}
+ for key in oldExpDesignY.keys():
+ NewExpDesignY[key] = np.vstack(
+ (oldExpDesignY[key], Y_PC_can[key])
+ )
+
+ engine_can.ExpDesign.sampling_method = 'user'
+ engine_can.ExpDesign.X = NewExpDesignX
+ # engine_can.ModelOutputDict = NewExpDesignY
+ engine_can.ExpDesign.Y = NewExpDesignY
+
+ # Train the model for the observed data using x_can
+ engine_can.MetaModel.input_obj.poly_coeffs_flag = False
+ engine_can.start_engine()
+ engine_can.train_normal(parallel=False)
+ engine_can.MetaModel.fit(NewExpDesignX, NewExpDesignY)
+ # engine_can.train_norm_design(parallel=False)
+
+ # Set the ExpDesign to its original values
+ engine_can.ExpDesign.X = oldExpDesignX
+ engine_can.ModelOutputDict = oldExpDesignY
+ engine_can.ExpDesign.Y = oldExpDesignY
+
+ if var.lower() == 'mi':
+ # Mutual information based on Krause et al.
+ # Adapted from Beck & Guillas (MICE) paper
+ _, std_PC_can = engine_can.MetaModel.eval_metamodel(samples=X_can)
+ std_can = {key: std_PC_can[key] for key in out_names}
+
+ std_old = {key: Y_std_can[key] for key in out_names}
+
+ varPCE = np.zeros((len(out_names)))
+ for i, key in enumerate(out_names):
+ varPCE[i] = np.mean(std_old[key] ** 2 / std_can[key] ** 2)
+ score = np.mean(varPCE)
+
+ return -1 * score
+
+ elif var.lower() == 'alc':
+ # Active learning based on Gramyc and Lee
+ # Adaptive design and analysis of supercomputer experiments Techno-
+ # metrics, 51 (2009), pp. 130–145.
+
+ # Evaluate the MetaModel at the given samples
+ Y_MC_can, Y_MC_std_can = engine_can.MetaModel.eval_metamodel(samples=X_MC)
+
+ # Compute the score
+ score = []
+ for i, key in enumerate(out_names):
+ pce_var = Y_MC_std_can[key] ** 2
+ pce_var_can = Y_MC_std[key] ** 2
+ score.append(np.mean(pce_var - pce_var_can, axis=0))
+ score = np.mean(score)
+
+ return -1 * score
+
+ # ---------- Inner MC simulation for computing Utility Value ----------
+ # Estimation of the integral via Monte Varlo integration
+ MCsize = X_MC.shape[0]
+ ESS = 0
+
+ likelihoods = None
+ while (ESS > MCsize) or (ESS < 1):
+
+ # Enriching Monte Carlo samples if need be
+ if ESS != 0:
+ X_MC = self.ExpDesign.generate_samples(
+ MCsize, 'random'
+ )
+
+ # Evaluate the MetaModel at the given samples
+ Y_MC, std_MC = PCE_Model_can.eval_metamodel(samples=X_MC)
+
+ # Likelihood computation (Comparison of data and simulation
+ # results via PCE with candidate design)
+ likelihoods = self._normpdf(
+ Y_MC, std_MC, self.observations, sigma2Dict
+ )
+
+ # Check the Effective Sample Size (1<ESS<MCsize)
+ ESS = 1 / np.sum(np.square(likelihoods / np.sum(likelihoods)))
+
+ # Enlarge sample size if it doesn't fulfill the criteria
+ if (ESS > MCsize) or (ESS < 1):
+ print("--- increasing MC size---")
+ MCsize *= 10
+ ESS = 0
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, MCsize)[0]
+
+ # Reject the poorly performed prior
+ accepted = (likelihoods / np.max(likelihoods)) >= unif
+
+ # -------------------- Utility functions --------------------
+ # Utility function Eq.2 in Ref. (2)
+ # Kullback-Leibler Divergence (Sergey's paper)
+ U_J_d = None
+ if var.lower() == 'dkl':
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods, dtype=np.longdouble)) # float128))
+
+ # Posterior-based expectation of likelihoods
+ # postLikelihoods = likelihoods[accepted]
+ # postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Haun et al implementation
+ U_J_d = np.mean(np.log(likelihoods[likelihoods != 0]) - logBME)
+
+ # U_J_d = np.sum(G_n_m_all)
+ # Ryan et al (2014) implementation
+ # importanceWeights = Likelihoods[Likelihoods!=0]/np.sum(Likelihoods[Likelihoods!=0])
+ # U_J_d = np.mean(importanceWeights*np.log(Likelihoods[Likelihoods!=0])) - logBME
+
+ # U_J_d = postExpLikelihoods - logBME
+
+ # Marginal likelihood
+ elif var.lower() == 'bme':
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods))
+ U_J_d = logBME
+
+ # Bayes risk likelihood
+ elif var.lower() == 'bayesrisk':
+
+ U_J_d = -1 * np.var(likelihoods)
+
+ # Entropy-based information gain
+ elif var.lower() == 'infentropy':
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods))
+
+ # Posterior-based expectation of likelihoods
+ postLikelihoods = likelihoods[accepted]
+ postLikelihoods /= np.nansum(likelihoods[accepted])
+ postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Posterior-based expectation of prior densities
+ logPriorLikelihoods = []
+ logPriorLikelihoods[accepted] = None # TODO: this is not defined here, just a fix
+ postExpPrior = np.mean(logPriorLikelihoods[accepted])
+
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
+
+ U_J_d = infEntropy * -1 # -1 for minimization
+
+ # D-Posterior-precision
+ elif var.lower() == 'dpp':
+ X_Posterior = X_MC[accepted]
+ # covariance of the posterior parameters
+ U_J_d = -np.log(np.linalg.det(np.cov(X_Posterior)))
+
+ # A-Posterior-precision
+ elif var.lower() == 'app':
+ X_Posterior = X_MC[accepted]
+ # trace of the posterior parameters
+ U_J_d = -np.log(np.trace(np.cov(X_Posterior)))
+
+ else:
+ print('The algorithm you requested has not been implemented yet!')
+
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+
+ return -1 * U_J_d # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def dual_annealing(self, method, Bounds, sigma2Dict, var, Run_No,
+ verbose=False):
+ """
+ Exploration algorithm to find the optimum parameter space.
+
+ Parameters
+ ----------
+ method : string
+ Exploitation method: `VarOptDesign`, `BayesActDesign` and
+ `BayesOptDesign`.
+ # TODO: BayesActDesign has no corresponding function call in this function!
+ Bounds : list of tuples
+ List of lower and upper boundaries of parameters.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : unknown
+ Run_No : int
+ Run number.
+ verbose : bool, optional
+ Print out a summary. The default is False.
+
+ Returns
+ -------
+ Run_No : int
+ Run number.
+ array
+ Optimial candidate.
+
+ """
+
+ Model = self.Model
+ max_func_itr = self.ExpDesign.max_func_itr
+
+ Res_Global = None
+ if method.lower() == 'varoptdesign':
+ Res_Global = opt.dual_annealing(self.util_VarBasedDesign,
+ bounds=Bounds,
+ args=(Model, var),
+ maxfun=max_func_itr)
+
+ elif method.lower() == 'bayesoptdesign':
+ Res_Global = opt.dual_annealing(self.util_BayesianDesign,
+ bounds=Bounds,
+ args=(Model, sigma2Dict, var),
+ maxfun=max_func_itr)
+
+ if verbose:
+ print(f"Global minimum: xmin = {Res_Global.x}, "
+ f"f(xmin) = {Res_Global.fun:.6f}, nfev = {Res_Global.nfev}")
+
+ return Run_No, Res_Global.x
+
+ # -------------------------------------------------------------------------
+ def util_AlphOptDesign(self, candidates, var='D-Opt'):
+ """
+ Enriches the Experimental design with the requested alphabetic
+ criterion based on exploring the space with number of sampling points.
+
+ Ref: Hadigol, M., & Doostan, A. (2018). Least squares polynomial chaos
+ expansion: A review of sampling strategies., Computer Methods in
+ Applied Mechanics and Engineering, 332, 382-407.
+
+ Arguments
+ ---------
+ candidates : int?
+ Number of candidate points to be searched
+
+ var : string
+ Alphabetic optimality criterion
+
+ Returns
+ -------
+ X_new : array of shape (1, n_params)
+ The new sampling location in the input space.
+ """
+ MetaModelOrig = self # TODO: this doesn't fully seem correct?
+ n_new_samples = MetaModelOrig.ExpDesign.n_new_samples
+ NCandidate = candidates.shape[0]
+
+ # TODO: Loop over outputs
+ OutputName = self.out_names[0]
+
+ # To avoid changes ub original aPCE object
+ # MetaModel = deepcopy(MetaModelOrig)
+
+ # Old Experimental design
+ oldExpDesignX = self.ExpDesign.X
+
+ # TODO: Only one psi can be selected.
+ # Suggestion: Go for the one with the highest LOO error
+ # TODO: this is just a patch, need to look at again!
+ Scores = list(self.MetaModel.score_dict['b_1'][OutputName].values())
+ ModifiedLOO = [1 - score for score in Scores]
+ outIdx = np.argmax(ModifiedLOO)
+
+ # Initialize Phi to save the criterion's values
+ Phi = np.zeros(NCandidate)
+
+ # TODO: also patched here
+ BasisIndices = self.MetaModel.basis_dict['b_1'][OutputName]["y_" + str(outIdx + 1)]
+ P = len(BasisIndices)
+
+ # ------ Old Psi ------------
+ univ_p_val = self.MetaModel.univ_basis_vals(oldExpDesignX)
+ Psi = create_psi(BasisIndices, univ_p_val)
+
+ # ------ New candidates (Psi_c) ------------
+ # Assemble Psi_c
+ univ_p_val_c = self.MetaModel.univ_basis_vals(candidates)
+ Psi_c = create_psi(BasisIndices, univ_p_val_c)
+
+ for idx in range(NCandidate):
+
+ # Include the new row to the original Psi
+ Psi_cand = np.vstack((Psi, Psi_c[idx]))
+
+ # Information matrix
+ PsiTPsi = np.dot(Psi_cand.T, Psi_cand)
+ M = PsiTPsi / (len(oldExpDesignX) + 1)
+
+ if 1e-12 < np.linalg.cond(PsiTPsi) < 1 / sys.float_info.epsilon:
+ # faster
+ invM = linalg.solve(M, sparse.eye(PsiTPsi.shape[0]).toarray())
+ else:
+ # stabler
+ invM = np.linalg.pinv(M)
+
+ # ---------- Calculate optimality criterion ----------
+ # Optimality criteria according to Section 4.5.1 in Ref.
+
+ # D-Opt
+ if var.lower() == 'd-opt':
+ Phi[idx] = (np.linalg.det(invM)) ** (1 / P)
+
+ # A-Opt
+ elif var.lower() == 'a-opt':
+ Phi[idx] = np.trace(invM)
+
+ # K-Opt
+ elif var.lower() == 'k-opt':
+ Phi[idx] = np.linalg.cond(M)
+
+ else:
+ # print(var.lower())
+ raise Exception('The optimality criterion you requested has '
+ 'not been implemented yet!')
+
+
+ return Phi
+
+ # -------------------------------------------------------------------------
+ def _normpdf(self, y_hat_pce, std_pce, obs_data, total_sigma2s,
+ rmse=None):
+ """
+ Calculated gaussian likelihood for given y+std based on given obs+sigma
+ # TODO: is this understanding correct?
+
+ Parameters
+ ----------
+ y_hat_pce : dict of 2d np arrays
+ Mean output of the surrogate.
+ std_pce : dict of 2d np arrays
+ Standard deviation output of the surrogate.
+ obs_data : dict of 1d np arrays
+ Observed data.
+ total_sigma2s : pandas dataframe, matches obs_data
+ Estimated uncertainty for the observed data.
+ rmse : dict, optional
+ RMSE values from validation of the surrogate. The default is None.
+
+ Returns
+ -------
+ likelihoods : dict of float
+ The likelihood for each surrogate eval in y_hat_pce compared to the
+ observations (?).
+
+ """
+
+ likelihoods = 1.0
+
+ # Loop over the outputs
+ for idx, out in enumerate(self.out_names):
+
+ # (Meta)Model Output
+ # print(y_hat_pce[out])
+ nsamples, nout = y_hat_pce[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout].values
+
+ # Surrogate error if valid dataset is given.
+ if rmse is not None:
+ tot_sigma2s += rmse[out] ** 2
+ else:
+ tot_sigma2s += np.mean(std_pce[out]) ** 2
+
+ likelihoods *= stats.multivariate_normal.pdf(
+ y_hat_pce[out], data, np.diag(tot_sigma2s),
+ allow_singular=True)
+
+ # TODO: remove this here
+ self.Likelihoods = likelihoods
+
+ return likelihoods
+
+ # -------------------------------------------------------------------------
+ def _corr_factor_BME(self, obs_data, total_sigma2s, logBME):
+ """
+ Calculates the correction factor for BMEs.
+ """
+ MetaModel = self.MetaModel
+ samples = self.ExpDesign.X # valid_samples
+ model_outputs = self.ExpDesign.Y # valid_model_runs
+ n_samples = samples.shape[0]
+
+ # Extract the requested model outputs for likelihood calulation
+ output_names = self.out_names
+
+ # TODO: Evaluate MetaModel on the experimental design and ValidSet
+ OutputRS, stdOutputRS = MetaModel.eval_metamodel(samples=samples)
+
+ logLik_data = np.zeros(n_samples)
+ logLik_model = np.zeros(n_samples)
+ # Loop over the outputs
+ for idx, out in enumerate(output_names):
+
+ # (Meta)Model Output
+ nsamples, nout = model_outputs[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout]
+
+ # Covariance Matrix
+ covMatrix_data = np.diag(tot_sigma2s)
+
+ for i, sample in enumerate(samples):
+ # Simulation run
+ y_m = model_outputs[out][i]
+
+ # Surrogate prediction
+ y_m_hat = OutputRS[out][i]
+
+ # CovMatrix with the surrogate error
+ # covMatrix = np.diag(stdOutputRS[out][i]**2)
+ # covMatrix = np.diag((y_m - y_m_hat) ** 2)
+ covMatrix = np.diag(
+ np.mean((model_outputs[out] - OutputRS[out]), axis=0) ** 2
+ )
+
+ # Compute likelilhood output vs data
+ logLik_data[i] += logpdf(
+ y_m_hat, data, covMatrix_data
+ )
+
+ # Compute likelilhood output vs surrogate
+ logLik_model[i] += logpdf(y_m_hat, y_m, covMatrix)
+
+ # Weight
+ logLik_data -= logBME
+ weights = np.exp(logLik_model + logLik_data)
+
+ return np.log(np.mean(weights))
+
+ # -------------------------------------------------------------------------
+ def _posteriorPlot(self, posterior, par_names, key):
+ """
+ Plot the posterior of a specific key as a corner plot
+
+ Parameters
+ ----------
+ posterior : 2d np.array
+ Samples of the posterior.
+ par_names : list of strings
+ List of the parameter names.
+ key : string
+ Output key that this posterior belongs to.
+
+ Returns
+ -------
+ figPosterior : corner.corner
+ Plot of the posterior.
+
+ """
+
+ # Initialization
+ newpath = r'Outputs_SeqPosteriorComparison/posterior'
+ os.makedirs(newpath, exist_ok=True)
+
+ bound_tuples = self.ExpDesign.bound_tuples
+ n_params = len(par_names)
+ font_size = 40
+ if n_params == 2:
+
+ figPosterior, ax = plt.subplots(figsize=(15, 15))
+
+ sns.kdeplot(x=posterior[:, 0], y=posterior[:, 1],
+ fill=True, ax=ax, cmap=plt.cm.jet,
+ clip=bound_tuples)
+ # Axis labels
+ plt.xlabel(par_names[0], fontsize=font_size)
+ plt.ylabel(par_names[1], fontsize=font_size)
+
+ # Set axis limit
+ plt.xlim(bound_tuples[0])
+ plt.ylim(bound_tuples[1])
+
+ # Increase font size
+ plt.xticks(fontsize=font_size)
+ plt.yticks(fontsize=font_size)
+
+ # Switch off the grids
+ plt.grid(False)
+
+ else:
+ import corner
+ figPosterior = corner.corner(posterior, labels=par_names,
+ title_fmt='.2e', show_titles=True,
+ title_kwargs={"fontsize": 12})
+
+ figPosterior.savefig(f'./{newpath}/{key}.pdf', bbox_inches='tight')
+ plt.close()
+
+ # Save the posterior as .npy
+ np.save(f'./{newpath}/{key}.npy', posterior)
+
+ return figPosterior
+
+ # -------------------------------------------------------------------------
+ def _BME_Calculator(self, obs_data, sigma2Dict, rmse=None):
+ """
+ This function computes the Bayesian model evidence (BME) via Monte
+ Carlo integration.
+
+ Parameters
+ ----------
+ obs_data : dict of 1d np arrays
+ Observed data.
+ sigma2Dict : pandas dataframe, matches obs_data
+ Estimated uncertainty for the observed data.
+ rmse : dict of floats, optional
+ RMSE values for each output-key. The dafault is None.
+
+ Returns
+ -------
+ (logBME, KLD, X_Posterior, Likelihoods, distHellinger)
+
+ """
+ # Initializations
+ # TODO: this just does not make sense, recheck from old commits
+ if self.valid_likelihoods is not None:
+ valid_likelihoods = self.valid_likelihoods
+ else:
+ valid_likelihoods = []
+ valid_likelihoods = np.array(valid_likelihoods)
+
+ post_snapshot = self.ExpDesign.post_snapshot
+ if post_snapshot or valid_likelihoods.shape[0] != 0:
+ newpath = r'Outputs_SeqPosteriorComparison/likelihood_vs_ref'
+ os.makedirs(newpath, exist_ok=True)
+
+ SamplingMethod = 'random'
+ MCsize = 10000
+ ESS = 0
+
+ # Estimation of the integral via Monte Varlo integration
+ while (ESS > MCsize) or (ESS < 1):
+
+ # Generate samples for Monte Carlo simulation
+ X_MC = self.ExpDesign.generate_samples(
+ MCsize, SamplingMethod
+ )
+
+ # Monte Carlo simulation for the candidate design
+ Y_MC, std_MC = self.MetaModel.eval_metamodel(samples=X_MC)
+
+ # Likelihood computation (Comparison of data and
+ # simulation results via PCE with candidate design)
+ Likelihoods = self._normpdf(
+ Y_MC, std_MC, obs_data, sigma2Dict, rmse
+ )
+
+ # Check the Effective Sample Size (1000<ESS<MCsize)
+ ESS = 1 / np.sum(np.square(Likelihoods / np.sum(Likelihoods)))
+
+ # Enlarge sample size if it doesn't fulfill the criteria
+ if (ESS > MCsize) or (ESS < 1):
+ print(f'ESS={ESS} MC size should be larger.')
+ MCsize *= 10
+ ESS = 0
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, MCsize)[0]
+
+ # Reject the poorly performed prior
+ accepted = (Likelihoods / np.max(Likelihoods)) >= unif
+ X_Posterior = X_MC[accepted]
+
+ # ------------------------------------------------------------
+ # --- Kullback-Leibler Divergence & Information Entropy ------
+ # ------------------------------------------------------------
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(Likelihoods))
+
+ # TODO: Correction factor
+ # log_weight = self.__corr_factor_BME(obs_data, sigma2Dict, logBME)
+
+ # Posterior-based expectation of likelihoods
+ postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
+
+ # Posterior-based expectation of prior densities
+ # TODO: this is commented out, as it is not used again
+ # postExpPrior = np.mean(
+ # np.log(self.ExpDesign.JDist.pdf(X_Posterior.T))
+ # )
+
+ # Calculate Kullback-Leibler Divergence
+ # KLD = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
+ KLD = postExpLikelihoods - logBME
+
+ # Information Entropy based on Entropy paper Eq. 38
+ # infEntropy = logBME - postExpPrior - postExpLikelihoods
+
+ # If post_snapshot is True, plot likelihood vs refrence
+ if post_snapshot or valid_likelihoods:
+ # Hellinger distance
+ valid_likelihoods = np.array(valid_likelihoods)
+ ref_like = np.log(valid_likelihoods[(valid_likelihoods > 0)])
+ est_like = np.log(Likelihoods[Likelihoods > 0])
+ distHellinger = hellinger_distance(ref_like, est_like)
+
+ idx = len([name for name in os.listdir(newpath) if 'Likelihoods_'
+ in name and os.path.isfile(os.path.join(newpath, name))])
+
+ fig, ax = plt.subplots()
+ try:
+ sns.kdeplot(np.log(valid_likelihoods[valid_likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]), shade=True,
+ color="b", label='Likelihood with PCE')
+ except:
+ pass
+
+ text = f"Hellinger Dist.={distHellinger:.3f}\n logBME={logBME:.3f}"
+ "\n DKL={KLD:.3f}"
+
+ plt.text(0.05, 0.75, text, bbox=dict(facecolor='wheat',
+ edgecolor='black',
+ boxstyle='round,pad=1'),
+ transform=ax.transAxes)
+
+ fig.savefig(f'./{newpath}/Likelihoods_{idx}.pdf',
+ bbox_inches='tight')
+ plt.close()
+
+ else:
+ distHellinger = 0.0
+
+ # Bayesian inference with Emulator only for 2D problem
+ if post_snapshot and self.MetaModel.n_params == 2 and not idx % 5:
+ BayesOpts = BayesInference(self)
+
+ BayesOpts.emulator = True
+ BayesOpts.plot_post_pred = False
+
+ # Select the inference method
+ import emcee
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters passed to self.mcmc_params
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e5,
+ 'n_walkers': 30,
+ 'moves': emcee.moves.KDEMove(),
+ 'verbose': False
+ }
+
+ # ----- Define the discrepancy model -------
+ # TODO: check with Farid if this first line is how it should be
+ BayesOpts.measured_data = obs_data
+ obs_data = pd.DataFrame(obs_data, columns=self.out_names)
+ BayesOpts.measurement_error = obs_data
+ # TODO: shouldn't the uncertainty be sigma2Dict instead of obs_data?
+
+ # # -- (Option B) --
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obs_data ** 2
+ BayesOpts.Discrepancy = DiscrepancyOpts
+ # Start the calibration/inference
+ Bayes_PCE = BayesOpts.create_inference()
+ X_Posterior = Bayes_PCE.posterior_df.values
+
+ return logBME, KLD, X_Posterior, Likelihoods, distHellinger
+
+ # -------------------------------------------------------------------------
+ def _validError(self):
+ """
+ Evaluate the metamodel on the validation samples and calculate the
+ error against the corresponding model runs
+
+ Returns
+ -------
+ rms_error : dict
+ RMSE for each validation run.
+ valid_error : dict
+ Normed (?)RMSE for each validation run.
+
+ """
+ # Extract the original model with the generated samples
+ valid_model_runs = self.ExpDesign.valid_model_runs
+
+ # Run the PCE model with the generated samples
+ valid_PCE_runs, _ = self.MetaModel.eval_metamodel(samples=self.ExpDesign.valid_samples)
+
+ rms_error = {}
+ valid_error = {}
+ # Loop over the keys and compute RMSE error.
+ for key in self.out_names:
+ rms_error[key] = mean_squared_error(
+ valid_model_runs[key], valid_PCE_runs[key],
+ multioutput='raw_values',
+ sample_weight=None,
+ squared=False)
+ # Validation error
+ valid_error[key] = (rms_error[key] ** 2)
+ valid_error[key] /= np.var(valid_model_runs[key], ddof=1, axis=0)
+
+ # Print a report table
+ print("\n>>>>> Updated Errors of {} <<<<<".format(key))
+ print("\nIndex | RMSE | Validation Error")
+ print('-' * 35)
+ print('\n'.join(f'{i + 1} | {k:.3e} | {j:.3e}' for i, (k, j)
+ in enumerate(zip(rms_error[key],
+ valid_error[key]))))
+
+ return rms_error, valid_error
+
+ # -------------------------------------------------------------------------
+ def _error_Mean_Std(self):
+ """
+ Calculates the error in the overall mean and std approximation of the
+ surrogate against the mc-reference provided to the model.
+ This can only be applied to metamodels of polynomial type
+
+ Returns
+ -------
+ RMSE_Mean : float
+ RMSE of the means
+ RMSE_std : float
+ RMSE of the standard deviations
+
+ """
+ # Compute the mean and std based on the MetaModel
+ pce_means, pce_stds = self.MetaModel._compute_pce_moments()
+
+ # Compute the root mean squared error
+ for output in self.out_names:
+ # Compute the error between mean and std of MetaModel and OrigModel
+ RMSE_Mean = mean_squared_error(
+ self.Model.mc_reference['mean'], pce_means[output], squared=False
+ )
+ RMSE_std = mean_squared_error(
+ self.Model.mc_reference['std'], pce_stds[output], squared=False
+ )
+
+ return RMSE_Mean, RMSE_std
+
+ def _select_indexes(self, prior_samples, collocation_points):
+ """
+ ToDo: This function will be used to check the user-input exploration samples, remove training points that
+ were already used, and select the first mc_size samples that have not yet been used for training. It should also
+ assign an exploration score of 0 to all samples.
+ Args:
+ prior_samples: array [mc_size, n_params]
+ Pre-defined samples from the parameter space, out of which the sample sets should be extracted.
+ collocation_points: [tp_size, n_params]
+ array with training points which were already used to train the surrogate model, and should therefore
+ not be re-explored.
+
+ Returns: array[self.mc_size,]
+ With indexes of the new candidate parameter sets, to be read from the prior_samples array
+
+ """
+ n_tp = collocation_points.shape[0]
+ # a) get index of elements that have already been used
+ aux1_ = np.where((prior_samples[:self.mc_samples + n_tp, :] == collocation_points[:, None]).all(-1))[1]
+ # b) give each element in the prior a True if it has not been used before
+ aux2_ = np.invert(np.in1d(np.arange(prior_samples[:self.mc_samples + n_tp, :].shape[0]), aux1_))
+ # c) Select the first d_size_bal elements in prior_sample that have not been used before
+ al_unique_index = np.arange(prior_samples[:self.mc_samples + n_tp, :].shape[0])[aux2_]
+ al_unique_index = al_unique_index[:self.mc_samples]
+
+ return al_unique_index
\ No newline at end of file
diff --git a/src/bayesvalidrox/surrogate_models/surrogate_models.py b/src/bayesvalidrox/surrogate_models/surrogate_models.py
index 3444d83f7e070caa32502d2484968a8f0f2b9891..157260d4b5432f847670a6804deac7dbfa8eb4bd 100644
--- a/src/bayesvalidrox/surrogate_models/surrogate_models.py
+++ b/src/bayesvalidrox/surrogate_models/surrogate_models.py
@@ -1005,6 +1005,7 @@ class MetaModel:
break
# Store the score in the scores list
+ print(qNormScores)
best_q = np.nanargmax(qNormScores)
scores[degIdx] = qNormScores[best_q]
diff --git a/tests/test_BayesInference.py b/tests/test_BayesInference.py
index c31a9830e7d7e4d186936d955920885adfd39300..4b37f2cbb2776b3c881599c98a2363bc42b3f0d0 100644
--- a/tests/test_BayesInference.py
+++ b/tests/test_BayesInference.py
@@ -22,6 +22,7 @@ class BayesInference:
_plot_max_a_posteriori Need working model to test this
_plot_post_predictive - x
"""
+
import sys
import pytest
import numpy as np
@@ -40,8 +41,6 @@ from bayesvalidrox.bayes_inference.mcmc import MCMC
from bayesvalidrox.bayes_inference.bayes_inference import BayesInference
from bayesvalidrox.bayes_inference.bayes_inference import _logpdf, _kernel_rbf
-import matplotlib as mpl
-mpl.rcParams.update(mpl.rcParamsDefault)
#%% Test _logpdf
@@ -913,7 +912,6 @@ def test_plot_log_BME() -> None:
engine = Engine(mm, mod, expdes)
bi = BayesInference(engine)
- #bi.log_BME = np.array([[0, 0.2], [0, 0.2]])
bi.log_BME = np.array([0, 0.2, 0, 0.2])
bi.n_tot_measurement = 1
bi.plot_log_BME()
diff --git a/tests/test_InputSpace.py b/tests/test_InputSpace.py
index 7703f1141c70fe028444debd9b17d4ecfed12adf..40f26956376d07e59161cff6418aab1cab2c898f 100644
--- a/tests/test_InputSpace.py
+++ b/tests/test_InputSpace.py
@@ -13,11 +13,12 @@ import sys
import pytest
import numpy as np
+sys.path.append("src/")
+sys.path.append("../src/")
+
from bayesvalidrox.surrogate_models.inputs import Input
from bayesvalidrox.surrogate_models.input_space import InputSpace
-sys.path.append("src/")
-sys.path.append("../src/")
#%% Test ExpDesign.check_valid_input
diff --git a/tests/test_MetaModel.py b/tests/test_MetaModel.py
index 3b67f6699e9867ef61264d2d45f4b61d24a660d8..5cea0dcae3601e56fa213bb3cb5ba4ffdc44d094 100644
--- a/tests/test_MetaModel.py
+++ b/tests/test_MetaModel.py
@@ -29,12 +29,13 @@ import numpy as np
import pytest
import sys
+sys.path.append("src/")
+
from bayesvalidrox.surrogate_models.inputs import Input
from bayesvalidrox.surrogate_models.input_space import InputSpace
from bayesvalidrox.surrogate_models.surrogate_models import MetaModel, corr_loocv_error, create_psi
from bayesvalidrox.surrogate_models.surrogate_models import gaussian_process_emulator
-sys.path.append("src/")
#%% Test MetaMod constructor on its own
@@ -207,7 +208,7 @@ def test_fit() -> None:
inp.Marginals[0].dist_type = 'normal'
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
def test_fit_parallel() -> None:
@@ -219,7 +220,7 @@ def test_fit_parallel() -> None:
inp.Marginals[0].dist_type = 'normal'
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]}, parallel=True)
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]}, parallel=True)
def test_fit_verbose() -> None:
@@ -231,7 +232,7 @@ def test_fit_verbose() -> None:
inp.Marginals[0].dist_type = 'normal'
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]}, verbose=True)
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]}, verbose=True)
def test_fit_pca() -> None:
@@ -244,7 +245,7 @@ def test_fit_pca() -> None:
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
mm.dim_red_method = 'pca'
- mm.fit([[0.2], [0.8]], {'Z': [[0.4, 0.4], [0.5, 0.6]]}, verbose=True)
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]}, verbose=True)
def test_fit_gpe() -> None:
@@ -257,7 +258,7 @@ def test_fit_gpe() -> None:
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
mm.meta_model_type = 'gpe'
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
#%% Test MetaModel.create_psi
@@ -768,8 +769,7 @@ def test_adaptive_regression_fewsamples() -> None:
with pytest.raises(AttributeError) as excinfo:
mm.adaptive_regression(outputs, 0)
- assert str(
- excinfo.value) == ('There are too few samples for the corrected loo-cv error. Fit surrogate on at least as '
+ assert str(excinfo.value) == ('There are too few samples for the corrected loo-cv error. Fit surrogate on at least as '
'many samples as parameters to use this')
@@ -1013,7 +1013,7 @@ def test_eval_metamodel() -> None:
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
mm.out_names = ['Z']
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
mm.eval_metamodel([[0.4]])
@@ -1028,7 +1028,7 @@ def test_eval_metamodel_normalboots() -> None:
mm = MetaModel(inp)
mm.bootstrap_method = 'normal'
mm.out_names = ['Z']
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
mm.eval_metamodel([[0.4]])
@@ -1043,7 +1043,7 @@ def test_eval_metamodel_highnormalboots() -> None:
mm = MetaModel(inp)
mm.n_bootstrap_itrs = 2
mm.out_names = ['Z']
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
mm.eval_metamodel([[0.4]])
@@ -1124,7 +1124,7 @@ def test__compute_pce_moments() -> None:
inp.Marginals[0].dist_type = 'normal'
inp.Marginals[0].parameters = [0, 1]
mm = MetaModel(inp)
- mm.fit([[0.2], [0.8]], {'Z': [[0.4], [0.5]]})
+ mm.fit([[0.2], [0.4], [0.8]], {'Z': [[0.4], [0.2], [0.5]]})
mm._compute_pce_moments()
diff --git a/tests/test_SequentialDesign.py b/tests/test_SequentialDesign.py
new file mode 100644
index 0000000000000000000000000000000000000000..5d713e747d47425f45e3fcbed8ace16073b53192
--- /dev/null
+++ b/tests/test_SequentialDesign.py
@@ -0,0 +1,904 @@
+# -*- coding: utf-8 -*-
+"""
+Test the SequentialDesign class for bayesvalidrox
+
+Tests are available for the following functions
+ logpdf - x
+ subdomain - x
+SequentialDesign:
+ start_seqdesign
+ choose_next_sample
+ plotter
+ tradoff_weights - x
+ run_util_func
+ util_VarBasedDesign
+ util_BayesianActiveDesign
+ util_BayesianDesign
+ dual_annealing
+ util_AlphOptDesign
+ _normpdf - x Also move outside the class?
+ _corr_factor_BME Not used again in this class
+ _posteriorPlot - x
+ _BME_Calculator - x
+ _validError - x
+ _error_Mean_Std - x
+ _select_indices
+
+
+"""
+
+import sys
+import pytest
+import numpy as np
+import pandas as pd
+
+sys.path.append("../src/")
+
+from bayesvalidrox.surrogate_models.inputs import Input
+from bayesvalidrox.surrogate_models.exp_designs import ExpDesigns
+from bayesvalidrox.surrogate_models.sequential_design import SequentialDesign
+from bayesvalidrox.surrogate_models.surrogate_models import MetaModel
+from bayesvalidrox.pylink.pylink import PyLinkForwardModel as PL
+from bayesvalidrox.surrogate_models.engine import Engine
+from bayesvalidrox.bayes_inference.discrepancy import Discrepancy
+
+#%% Test Engine.tradeoff_weights
+
+def test_tradeoff_weights_None() -> None:
+ """
+ Tradeoff weights with no scheme
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ mm = MetaModel(inp)
+ expdes = ExpDesigns(inp)
+ mod = PL()
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ weights = seqDes.tradeoff_weights(None, [[0], [1]], {'Z': [[0.4], [0.5]]})
+ assert weights[0] == 0 and weights[1] == 1
+
+
+def test_tradeoff_weights_equal() -> None:
+ """
+ Tradeoff weights with 'equal' scheme
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ mm = MetaModel(inp)
+ expdes = ExpDesigns(inp)
+ mod = PL()
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ weights = seqDes.tradeoff_weights('equal', [[0], [1]], {'Z': [[0.4], [0.5]]})
+ assert weights[0] == 0.5 and weights[1] == 0.5
+
+
+def test_tradeoff_weights_epsdecr() -> None:
+ """
+ Tradeoff weights with 'epsilon-decreasing' scheme
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ mm = MetaModel(inp)
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 3
+ expdes.X = np.array([[0], [1]])
+ mod = PL()
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ weights = seqDes.tradeoff_weights('epsilon-decreasing', expdes.X, {'Z': [[0.4], [0.5]]})
+ assert weights[0] == 1.0 and weights[1] == 0.0
+
+
+def test_tradeoff_weights_adaptive() -> None:
+ """
+ Tradeoff weights with 'adaptive' scheme
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ mm = MetaModel(inp)
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 3
+ expdes.X = np.array([[0], [1]])
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ weights = seqDes.tradeoff_weights('adaptive', expdes.X, {'Z': [[0.4], [0.5]]})
+ assert weights[0] == 0.5 and weights[1] == 0.5
+
+
+def test_tradeoff_weights_adaptiveit1() -> None:
+ """
+ Tradeoff weights with 'adaptive' scheme for later iteration (not the first)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes._y_hat_prev, _ = mm.eval_metamodel(samples=np.array([[0.1], [0.2], [0.6]]))
+ seqDes.tradeoff_weights('adaptive', expdes.X, expdes.Y)
+
+
+
+#%% Test Engine.choose_next_sample
+
+def test_choose_next_sample() -> None:
+ """
+ Chooses new sample using all standard settings (exploration, random, space-filling,...)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'random'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample()
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_da_spaceparallel() -> None:
+ """
+ Chooses new sample using dual-annealing and space-filling, parallel=True
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'dual-annealing'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.parallel = True
+ x, nan = seqDes.choose_next_sample()
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_da_spacenoparallel() -> None:
+ """
+ Chooses new sample using dual-annealing and space-filling, parallel = False
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'dual-annealing'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.parallel = False
+ x, nan = seqDes.choose_next_sample()
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_loo_space() -> None:
+ """
+ Chooses new sample using all LOO-CV and space-filling
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'LOO-CV'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample()
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_vor_space() -> None:
+ """
+ Chooses new sample using voronoi, space-filling
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'voronoi'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ #x, nan = seqDes.choose_next_sample()
+ #assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+ # TODO: removed this functionality for v1.1.0
+ with pytest.raises(AttributeError) as excinfo:
+ x, nan = seqDes.choose_next_sample()
+ assert str(excinfo.value) == ('Exploration with voronoi currently not supported!')
+
+def test_choose_next_sample_latin_space() -> None:
+ """
+ Chooses new sample using all latin-hypercube, space-filling
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'Space-filling'
+ expdes.util_func = 'Space-filling'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample()
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_alphD() -> None:
+ """
+ Chooses new sample using all latin-hypercube, alphabetic (D)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'alphabetic'
+ expdes.util_func = 'D-Opt'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_alphK() -> None:
+ """
+ Chooses new sample using all latin-hypercube, alphabetic (K)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'alphabetic'
+ expdes.util_func = 'K-Opt'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_alphA() -> None:
+ """
+ Chooses new sample using all latin-hypercube, alphabetic (A)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'alphabetic'
+ expdes.util_func = 'A-Opt'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_VarALM() -> None:
+ """
+ Chooses new sample using all latin-hypercube, VarDesign (ALM)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'VarOptDesign'
+ expdes.util_func = 'ALM'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_VarEIGF() -> None:
+ """
+ Chooses new sample using all latin-hypercube, VarDesign (EIGF)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'VarOptDesign'
+ expdes.util_func = 'EIGF'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+# TODO: shape mismatch for the total score
+if 0:
+ def test_choose_next_sample_latin_VarLOO() -> None:
+ """
+ Chooses new sample using all latin-hypercube, VarDesign (LOOCV)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'VarOptDesign'
+ expdes.util_func = 'LOOCV'
+
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ x, nan = seqDes.choose_next_sample(var=expdes.util_func)
+ assert x.shape[0] == 1 and x.shape[1] == 1
+
+
+def test_choose_next_sample_latin_BODMI() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (MI)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.sampling_method = 'user'
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'MI'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+def test_choose_next_sample_vor_BODMI() -> None:
+ """
+ Chooses new sample using all voronoi, BayesOptDesign (MI)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.sampling_method = 'user'
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'voronoi'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'MI'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+
+ # TODO: removed this functionality for v1.1.0
+ with pytest.raises(AttributeError) as excinfo:
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+ assert str(excinfo.value) == ('Exploration with voronoi currently not supported!')
+
+
+
+def test_choose_next_sample_latin_BODALC() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (ALC)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'ALC'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+def test_choose_next_sample_latin_BODDKL() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (DKL)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'DKL'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+def test_choose_next_sample_latin_BODDPP() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (DPP)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'DPP'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+def test_choose_next_sample_latin_BODAPP() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (APP)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'APP'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+def test_choose_next_sample_latin_BODMI_() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesOptDesign (MI)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesOptDesign'
+ expdes.util_func = 'MI'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+if 0:
+ def test_choose_next_sample_latin_BADBME() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesActDesign (BME)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesActDesign'
+ expdes.util_func = 'BME'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.n_obs = 1
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+ def test_choose_next_sample_latin_BADDKL() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesActDesign (DKL)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesActDesign'
+ expdes.util_func = 'DKL'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.n_obs = 1
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+ def test_choose_next_sample_latin_BADinfEntropy() -> None:
+ """
+ Chooses new sample using all latin-hypercube, BayesActDesign (infEntropy)
+ """
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ expdes = ExpDesigns(inp)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.tradeoff_scheme = 'equal'
+ expdes.explore_method = 'latin-hypercube'
+ expdes.exploit_method = 'BayesActDesign'
+ expdes.util_func = 'infEntropy'
+ mm = MetaModel(inp)
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
+ mod = PL()
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+ seqDes.out_names = ['Z']
+ seqDes.observations = {'Z': np.array([0.45])}
+ # seqDes.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ seqDes.n_obs = 1
+ seqDes.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
+
+
+
+#%% Main runs
+if __name__ == '__main__':
+ inp = Input()
+ inp.add_marginals()
+ inp.Marginals[0].dist_type = 'normal'
+ inp.Marginals[0].parameters = [0, 1]
+ # prior_samples = np.swapaxes(np.array([np.random.normal(0,1,10)]),0,1)
+
+ expdes = ExpDesigns(inp)
+ expdes.init_param_space(max_deg=1)
+ expdes.n_init_samples = 2
+ expdes.n_max_samples = 4
+ expdes.X = np.array([[0], [1], [0.5]])
+ expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
+ expdes.x_values = np.array([0]) # Error in plots if this is not
+
+ mm = MetaModel(inp)
+ mm.n_params = 1
+ mm.fit(expdes.X, expdes.Y)
+ expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(1))
+ # y_hat, y_std = mm.eval_metamodel(prior_samples)
+
+ mod = PL()
+ mod.observations = {'Z': np.array([0.45])}
+ mod.observations = {'Z': np.array([0.45]), 'x_values': np.array([0])} # Error if x_values not given
+ mod.Output.names = ['Z']
+ mod.n_obs = 1
+
+
+ engine = Engine(mm, mod, expdes)
+ engine.start_engine()
+ seqDes = SequentialDesign(mm, mod, expdes, engine)
+
+ sigma2Dict = {'Z': np.array([0.05])}
+ sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
+ obsData = pd.DataFrame({'Z': np.array([0.45]), 'x_values': np.array([0])}, columns=mod.Output.names)
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = (obsData * 0.15) ** 2
+ DiscrepancyOpts.opt_sigma = 'B'
diff --git a/tests/test_engine.py b/tests/test_engine.py
index 5e9c5efe768a43246c0618e66ee00e941f57cabc..780d64417f888a8d94e8fcce145f60d55561b437 100644
--- a/tests/test_engine.py
+++ b/tests/test_engine.py
@@ -370,702 +370,3 @@ def test_subdomain() -> None:
"""
subdomain([(0, 1), (0, 1)], 2)
-
-#%% Test Engine.tradeoff_weights
-
-def test_tradeoff_weights_None() -> None:
- """
- Tradeoff weights with no scheme
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- mm = MetaModel(inp)
- expdes = ExpDesigns(inp)
- mod = PL()
- engine = Engine(mm, mod, expdes)
- weights = engine.tradeoff_weights(None, [[0], [1]], {'Z': [[0.4], [0.5]]})
- assert weights[0] == 0 and weights[1] == 1
-
-
-def test_tradeoff_weights_equal() -> None:
- """
- Tradeoff weights with 'equal' scheme
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- mm = MetaModel(inp)
- expdes = ExpDesigns(inp)
- mod = PL()
- engine = Engine(mm, mod, expdes)
- weights = engine.tradeoff_weights('equal', [[0], [1]], {'Z': [[0.4], [0.5]]})
- assert weights[0] == 0.5 and weights[1] == 0.5
-
-
-def test_tradeoff_weights_epsdecr() -> None:
- """
- Tradeoff weights with 'epsilon-decreasing' scheme
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- mm = MetaModel(inp)
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 3
- expdes.X = np.array([[0], [1]])
- mod = PL()
- engine = Engine(mm, mod, expdes)
- weights = engine.tradeoff_weights('epsilon-decreasing', expdes.X, {'Z': [[0.4], [0.5]]})
- assert weights[0] == 1.0 and weights[1] == 0.0
-
-
-def test_tradeoff_weights_adaptive() -> None:
- """
- Tradeoff weights with 'adaptive' scheme
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- mm = MetaModel(inp)
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 3
- expdes.X = np.array([[0], [1]])
- mod = PL()
- engine = Engine(mm, mod, expdes)
- weights = engine.tradeoff_weights('adaptive', expdes.X, {'Z': [[0.4], [0.5]]})
- assert weights[0] == 0.5 and weights[1] == 0.5
-
-
-def test_tradeoff_weights_adaptiveit1() -> None:
- """
- Tradeoff weights with 'adaptive' scheme for later iteration (not the first)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine._y_hat_prev, _ = mm.eval_metamodel(samples=np.array([[0.1], [0.2], [0.6]]))
- engine.tradeoff_weights('adaptive', expdes.X, expdes.Y)
-
-
-#%% Test Engine.choose_next_sample
-
-def test_choose_next_sample() -> None:
- """
- Chooses new sample using all standard settings (exploration, random, space-filling,...)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'random'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_da_spaceparallel() -> None:
- """
- Chooses new sample using dual-annealing and space-filling, parallel=True
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'dual-annealing'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.parallel = True
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_da_spacenoparallel() -> None:
- """
- Chooses new sample using dual-annealing and space-filling, parallel = False
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'dual-annealing'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.parallel = False
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_loo_space() -> None:
- """
- Chooses new sample using all LOO-CV and space-filling
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'LOO-CV'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_vor_space() -> None:
- """
- Chooses new sample using voronoi, space-filling
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'voronoi'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_space() -> None:
- """
- Chooses new sample using all latin-hypercube, space-filling
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'Space-filling'
- expdes.util_func = 'Space-filling'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample()
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_alphD() -> None:
- """
- Chooses new sample using all latin-hypercube, alphabetic (D)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'alphabetic'
- expdes.util_func = 'D-Opt'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_alphK() -> None:
- """
- Chooses new sample using all latin-hypercube, alphabetic (K)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'alphabetic'
- expdes.util_func = 'K-Opt'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_alphA() -> None:
- """
- Chooses new sample using all latin-hypercube, alphabetic (A)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'alphabetic'
- expdes.util_func = 'A-Opt'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_VarALM() -> None:
- """
- Chooses new sample using all latin-hypercube, VarDesign (ALM)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'VarOptDesign'
- expdes.util_func = 'ALM'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_VarEIGF() -> None:
- """
- Chooses new sample using all latin-hypercube, VarDesign (EIGF)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'VarOptDesign'
- expdes.util_func = 'EIGF'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-# TODO: shape mismatch for the total score
-if 0:
- def test_choose_next_sample_latin_VarLOO() -> None:
- """
- Chooses new sample using all latin-hypercube, VarDesign (LOOCV)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'VarOptDesign'
- expdes.util_func = 'LOOCV'
-
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- x, nan = engine.choose_next_sample(var=expdes.util_func)
- assert x.shape[0] == 1 and x.shape[1] == 1
-
-
-def test_choose_next_sample_latin_BODMI() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (MI)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.sampling_method = 'user'
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'MI'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
-def test_choose_next_sample_latin_BODALC() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (ALC)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'ALC'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
-def test_choose_next_sample_latin_BODDKL() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (DKL)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'DKL'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
-def test_choose_next_sample_latin_BODDPP() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (DPP)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'DPP'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
-def test_choose_next_sample_latin_BODAPP() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (APP)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'APP'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
-def test_choose_next_sample_latin_BODMI_() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesOptDesign (MI)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesOptDesign'
- expdes.util_func = 'MI'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-if 0:
- def test_choose_next_sample_latin_BADBME() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesActDesign (BME)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesActDesign'
- expdes.util_func = 'BME'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.n_obs = 1
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
- def test_choose_next_sample_latin_BADDKL() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesActDesign (DKL)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesActDesign'
- expdes.util_func = 'DKL'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.n_obs = 1
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)
-
-
- def test_choose_next_sample_latin_BADinfEntropy() -> None:
- """
- Chooses new sample using all latin-hypercube, BayesActDesign (infEntropy)
- """
- inp = Input()
- inp.add_marginals()
- inp.Marginals[0].dist_type = 'normal'
- inp.Marginals[0].parameters = [0, 1]
- expdes = ExpDesigns(inp)
- expdes.n_init_samples = 2
- expdes.n_max_samples = 4
- expdes.X = np.array([[0], [1], [0.5]])
- expdes.Y = {'Z': [[0.4], [0.5], [0.45]]}
- expdes.tradeoff_scheme = 'equal'
- expdes.explore_method = 'latin-hypercube'
- expdes.exploit_method = 'BayesActDesign'
- expdes.util_func = 'infEntropy'
- mm = MetaModel(inp)
- mm.fit(expdes.X, expdes.Y)
- expdes.generate_ED(expdes.n_init_samples, max_pce_deg=np.max(mm.pce_deg))
- mod = PL()
- engine = Engine(mm, mod, expdes)
- engine.out_names = ['Z']
- engine.observations = {'Z': np.array([0.45])}
- # engine.choose_next_sample(sigma2=None, n_candidates=5, var='DKL')
- sigma2Dict = {'Z': np.array([0.05])}
- sigma2Dict = pd.DataFrame(sigma2Dict, columns=['Z'])
- engine.n_obs = 1
- engine.choose_next_sample(sigma2=sigma2Dict, var=expdes.util_func)