diff --git a/examples/model-comparison/L2_model.py b/examples/model-comparison/L2_model.py
index e945c6888593d257d68d5af258c00a2020ca4c83..6b28c818101e25859bdb222b82cfd9bee741d381 100644
--- a/examples/model-comparison/L2_model.py
+++ b/examples/model-comparison/L2_model.py
@@ -3,14 +3,14 @@
"""
This is a simple linear model.
-The code for this numerical experiments is available at https://github.com/MichaelSinsbeck/
-paper sequential-design-model-selection.
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
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/
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
Pfaffenwaldring 61
70569 Stuttgart
@@ -24,7 +24,11 @@ def L2_model(xx):
"""
Linear model y = a*x+b
- Models adapted from Anneli Guthke
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
Parameters
----------
diff --git a/examples/model-comparison/NL2_model.py b/examples/model-comparison/NL2_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..5fd4820e76a9756b85b891b0d8272404e81d3361
--- /dev/null
+++ b/examples/model-comparison/NL2_model.py
@@ -0,0 +1,57 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This is a nonlinear cosine model.
+
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
+
+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 Oct 8 2021
+
+"""
+import numpy as np
+
+
+def NL2_model(xx):
+ """
+ Nonlinear model y = exp(a*x) + b
+
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
+
+ Parameters
+ ----------
+ xx : array
+ Parameters a and b.
+
+ Returns
+ -------
+ 2D-array
+ The first row contains the measurement locations.
+ The second row contains the model outputs.
+
+ """
+ n_output = 15
+ meas_loc = np.linspace(0.25, 4.75, n_output)
+
+ # NL2_model
+ NL2_model = np.exp(xx[:, 0] * meas_loc) + xx[:, 1]
+
+ # Output
+ output = {
+ 'x_values': meas_loc,
+ 'Z': NL2_model
+ }
+
+ return output
diff --git a/examples/model-comparison/NL4_model.py b/examples/model-comparison/NL4_model.py
index 2a1cc14e154e0baf34c7515ae2d65e6522391dfb..5ca495306d9a6d277ec654a3efbdfb84bfc28ce1 100644
--- a/examples/model-comparison/NL4_model.py
+++ b/examples/model-comparison/NL4_model.py
@@ -3,14 +3,14 @@
"""
This is a nonlinear cosine model.
-The code for this numerical experiments is available at https://github.com/MichaelSinsbeck/
-paper sequential-design-model-selection.
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
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/
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
Pfaffenwaldring 61
70569 Stuttgart
@@ -24,7 +24,11 @@ def NL4_model(xx):
"""
Nonlinear model y = a*cos(b*x+c)+d
- Models adapted from Anneli Guthke
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
Parameters
----------
diff --git a/examples/model-comparison/test_model_comparison.py b/examples/model-comparison/test_model_comparison.py
index a55d86afc8227d9dcf77a6e658ed21a4ea314235..4bdba4562f1b0fa5ca88970075f1697872211783 100644
--- a/examples/model-comparison/test_model_comparison.py
+++ b/examples/model-comparison/test_model_comparison.py
@@ -34,6 +34,7 @@ from bayes_inference.discrepancy import Discrepancy
if __name__ == "__main__":
+ # Read data
sigma = 0.6
data = {
'x [m]': np.linspace(0.25, 4.75, 15),
@@ -49,16 +50,26 @@ if __name__ == "__main__":
myL2Model.link_type = 'Function'
myL2Model.py_file = 'L2_model'
- myL2Model.name = 'L2_model'
+ myL2Model.name = 'linear'
myL2Model.Output.names = ['Z']
myL2Model.observations = data
+ # -- Nonlinear exponential model -------
+ myNL2Model = PyLinkForwardModel()
+
+ myNL2Model.link_type = 'Function'
+ myNL2Model.py_file = 'NL2_model'
+ myNL2Model.name = 'exponential'
+ myNL2Model.Output.names = ['Z']
+ myNL2Model.observations = data
+
# ------ Nonlinear cosine model ---------
+ # Data generating process
myNL4Model = PyLinkForwardModel()
myNL4Model.link_type = 'Function'
myNL4Model.py_file = 'NL4_model'
- myNL4Model.name = 'NL4_model'
+ myNL4Model.name = 'cosine'
myNL4Model.Output.names = ['Z']
myNL4Model.observations = data
@@ -83,14 +94,30 @@ if __name__ == "__main__":
L2_Inputs.Marginals[i].name = f'$X_{i+1}$'
L2_Inputs.Marginals[i].input_data = L2_input_params[:, i]
+ # ------ Nonlinear exponential model ---------
+ NL2_Inputs = Input()
+ NL2_prior_mean = np.array([0.4, -0.3])
+ NL2_prior_cov = np.array(
+ [[0.003, -0.0001],
+ [-0.0001, 0.03]]
+ )
+ NL2_input_params = np.random.multivariate_normal(
+ NL2_prior_mean, NL2_prior_cov, size=n_sample
+ )
+
+ for i in range(NL2_input_params.shape[1]):
+ NL2_Inputs.add_marginals()
+ NL2_Inputs.Marginals[i].name = f'$X_{i+1}$'
+ NL2_Inputs.Marginals[i].input_data = NL2_input_params[:, i]
+
# ------ Nonlinear cosine model ---------
NL4_Inputs = Input()
NL4_prior_mean = np.array([2.6, 0.5, -2.8, 2.3])
NL4_prior_cov = np.array(
- [[0.46, -0.07, 0.24, -0.14],
- [-0.07, 0.04, -0.05, 0.02],
- [0.24, -0.05, 0.30, -0.16],
- [-0.14, 0.02, -0.16, 0.30]]
+ [[0.44, -0.07, 0.24, -0.14],
+ [-0.07, 0.02, -0.05, 0.02],
+ [0.24, -0.05, 0.21, -0.16],
+ [-0.14, 0.02, -0.16, 0.28]]
)
NL4_input_params = np.random.multivariate_normal(
NL4_prior_mean, NL4_prior_cov, size=n_sample
@@ -151,18 +178,22 @@ if __name__ == "__main__":
# 6) chebyshev(FT) 7) grid(FT) 8)user
L2_MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
+ # ------ Nonlinear cosine model ---------
+ NL2_MetaModelOpts = L2_MetaModelOpts.copy_meta_model_opts(NL2_Inputs)
+
# ------ Nonlinear cosine model ---------
NL4_MetaModelOpts = L2_MetaModelOpts.copy_meta_model_opts(NL4_Inputs)
# >>>>>> Train the Surrogates <<<<<<<<<<<
L2_MetaModel = L2_MetaModelOpts.create_metamodel(myL2Model)
+ NL2_MetaModel = NL2_MetaModelOpts.create_metamodel(myNL2Model)
NL4_MetaModel = NL4_MetaModelOpts.create_metamodel(myNL4Model)
# =====================================================
# ========= POST PROCESSING OF METAMODELS ===========
# =====================================================
# ---------- Linear model -------------
- L2_PostPCE = PostProcessing(L2_MetaModel)
+ L2_PostPCE = PostProcessing(L2_MetaModel, name=myL2Model.name)
# Plot to check validation visually.
L2_PostPCE.valid_metamodel(n_samples=3)
@@ -176,8 +207,23 @@ if __name__ == "__main__":
# Plot the sobol indices
sobol_cell, total_sobol = L2_PostPCE.sobol_indices()
+ # ---------- Linear model -------------
+ NL2_PostPCE = PostProcessing(NL2_MetaModel, name=myNL2Model.name)
+
+ # Plot to check validation visually.
+ NL2_PostPCE.valid_metamodel(n_samples=3)
+
+ # Plot moments
+ NL2_PostPCE.plot_moments()
+
+ # Compute and print RMSE error
+ NL2_PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the sobol indices
+ sobol_cell, total_sobol = NL2_PostPCE.sobol_indices()
+
# ------ Nonlinear cosine model ---------
- NL4_PostPCE = PostProcessing(NL4_MetaModel)
+ NL4_PostPCE = PostProcessing(NL4_MetaModel, name=myNL4Model.name)
# Plot to check validation visually.
NL4_PostPCE.valid_metamodel(n_samples=3)
@@ -202,8 +248,9 @@ if __name__ == "__main__":
# ----- Define the options model -------
metaModels = {
- "L2_model": L2_MetaModel,
- "NL4_model": NL4_MetaModel
+ "linear": L2_MetaModel,
+ "exponential": NL4_MetaModel,
+ "cosine": NL4_MetaModel
}
# MCMC inference method
@@ -224,7 +271,7 @@ if __name__ == "__main__":
# BME Bootstrap
OptsDict_Bootstrap = {
"bootstrap": True,
- "n_samples": 20000,
+ "n_samples": 500000,
"Discrepancy": DiscrepancyOpts,
"emulator": False,
"plot_post_pred": False