From b7658e1ba0d69bad0b46798d998817b76473418c Mon Sep 17 00:00:00 2001 From: kohlhaasrebecca <rebecca.kohlhaas@outlook.com> Date: Mon, 3 Jun 2024 17:17:16 +0200 Subject: [PATCH] Rebuild --- docs/build/doctrees/al_description.doctree | Bin 0 -> 3031 bytes docs/build/doctrees/al_training.doctree | Bin 0 -> 2619 bytes docs/build/doctrees/bayes_description.doctree | Bin 0 -> 2983 bytes docs/build/doctrees/model_description.doctree | Bin 0 -> 13603 bytes docs/build/doctrees/post_description.doctree | Bin 2660 -> 14143 bytes .../doctrees/surrogate_description.doctree | Bin 2510 -> 20584 bytes docs/build/html/.buildinfo | 2 +- ...erence.bayes_inference.BayesInference.html | 16 +- ...idrox.bayes_inference.bayes_inference.html | 16 +- ...model_comparison.BayesModelComparison.html | 18 +- ...ayes_inference.bayes_model_comparison.html | 18 +- ...yes_inference.discrepancy.Discrepancy.html | 16 +- ...svalidrox.bayes_inference.discrepancy.html | 16 +- .../bayesvalidrox.bayes_inference.html | 18 +- 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a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html index 4f5997901..044b88f8e 100644 --- a/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html +++ b/docs/build/html/_autosummary/bayesvalidrox.surrogate_models.bayes_linear.gamma_mean.html @@ -10,7 +10,7 @@ <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=362ab14a" /> <link rel="stylesheet" type="text/css" href="../_static/styles/furo.css?v=135e06be" /> <link rel="stylesheet" type="text/css" href="../_static/styles/furo-extensions.css?v=36a5483c" /> - <link rel="stylesheet" type="text/css" href="../_static/custom.css?v=da48c412" /> + <link rel="stylesheet" type="text/css" href="../_static/custom.css?v=3c2b257a" /> @@ -164,8 +164,14 @@ </form> <div id="searchbox"></div><div class="sidebar-scroll"><div class="sidebar-tree"> <ul class="current"> +<li 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used in active learning in BayesValidRox. \ No newline at end of file diff --git a/docs/build/html/_sources/al_training.rst.txt b/docs/build/html/_sources/al_training.rst.txt new file mode 100644 index 000000000..e5a68dc7f --- /dev/null +++ b/docs/build/html/_sources/al_training.rst.txt @@ -0,0 +1,2 @@ +Active learning: iteratively expanding the training set +******************************************************* \ No newline at end of file diff --git a/docs/build/html/_sources/bayes_description.rst.txt b/docs/build/html/_sources/bayes_description.rst.txt new file mode 100644 index 000000000..2cfd3a6a8 --- /dev/null +++ b/docs/build/html/_sources/bayes_description.rst.txt @@ -0,0 +1,7 @@ +Bayesian inference and multi-model comparison +********************************************* + + +.. image:: ../diagrams/bayesian_validation.png + :width: 300 + :alt: UML diagram for classes related to Bayesian inference and multi-model comparison. diff --git a/docs/build/html/_sources/model_description.rst.txt b/docs/build/html/_sources/model_description.rst.txt new file mode 100644 index 000000000..f08ea0cd2 --- /dev/null +++ b/docs/build/html/_sources/model_description.rst.txt @@ -0,0 +1,54 @@ +Models +****** + +.. container:: twocol + + .. container:: leftside + + BayesValidRox gives options to create interfaces for a variety of models with the class :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel`. + + Its main function is to run the model on given samples and to read in and contain MC references and observations. + + Models can be defined via python functions, shell commands or as general executables. + This allows for the use of BayesValidRox with a broad range of models and easy extension to models that are defined with e.g. UM-Bridge. + + .. container:: rightside + + .. image:: ../diagrams/model.png + :width: 150 + :alt: UML diagram for the bayesvalidrox class :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel`. + +Example +======= +For this example we use a very simple model that maps the uncertain parameter :math:`X` from the example in :any:`input_description` to two outputs, the original value and its square. +We define this model as a function ``model`` in a new file ``model.py``. +This function takes a single realization of the uncertain parameter as a 2-dimensional ``np.array`` and returns a dictionary of model results. +Here we use the key ``A`` for the sample values and ``B`` for their squares. +Under the key ``x_values`` a list should be given that is of the same length as each output of the model for a single input. +The values in this list can denote e.g. timesteps and are used in postprocessing as labels of the x-axis. + +>>> def model(sample): +>>> square = sample*sample +>>> outputs = {'A': sample, 'B': square, 'x_values': [0]} +>>> return outputs + +In the main python file we can create an object of :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel` that links to this model. + +>>> from bayesvalidrox import PyLinkForwardModel + +We create an object of this class and set the ``link_type`` as 'Function' to indicate that this is a function in a python file. +``py_file`` should be set to the filename of the model and ``name`` to the name of the function. +Lastly we list the keys of the outputs that we are interested in. + +>>> Model = PyLinkForwardModel() +>>> Model.link_type = 'Function' +>>> Model.py_file = 'model' +>>> Model.name = 'model' +>>> Model.Output.names = ['A', 'B'] + +With this we have completed an interface to our model. +We can now evaluate this model on the samples created in the input example. + +>>> output, samples = Model.run_model_parallel(samples) + +Other types of model links can be found in :any:`examples`, e.g. :any:`beam` uses a shell command and parser. diff --git a/docs/build/html/_sources/post_description.rst.txt b/docs/build/html/_sources/post_description.rst.txt index 9950c8cf9..af2172709 100644 --- a/docs/build/html/_sources/post_description.rst.txt +++ b/docs/build/html/_sources/post_description.rst.txt @@ -1,2 +1,66 @@ -Postprocessing, Bayesian inference and Bayesian model comparison -**************************************************************** \ No newline at end of file +Postprocessing +************** +.. container:: twocol + + .. container:: leftside + + Postprocessing refers to evaluations and checks performed on a model to get an understanding of its properties and estimate its quality. + The BayesValidRox class :any:`bayesvalidrox.post_processing.post_processing.PostProcessing` includes functions that are applicable to all types of surrogate model. + + * ``valid_metamodel``: visualizing some metamodel runs against the corresponding model runs + * ``check_accuracy``: computing the RMSE error of the surrogate model + + .. container:: rightside + + .. image:: ../diagrams/postprocessing.png + :width: 300 + :alt: UML diagram for the classes and functions used in active learning in BayesValidRox. + +Postprocessing methods that are specific to a type of surrogate or training include + +* ``plot_moments``: visualizing the moments of a polynomial chaos expansion (PCE, aPCE) +* ``sobol_indices``: calculating the Sobol' and Total Sobol' indices (PCE, aPCE) +* ``plot_seq_design_diagnostics``: visualizing diagnostics that were evaluated during sequential training (surrogate trained with ``train_sequential``) + + +Example +======= +We want to compare out trained surrogate from :any:`al_description` against its original model. + +>>> from bayesvalidrox import PostProcessing + +The postprocessing object expects the full engine. This allows it to perform both sampling, running the model and running the surrogate model. + +>>> PostProc = PostProcessing(Engine_) + +To gain an understanding of the approximation quality we use both ``valid_metamodel`` and ``check_accuracy``. + +>>> PostProc.valid_metamodel(n_samples=1) +>>> PostProc.check_accuracy(n_samples=10) + +The visual comparison of model and metamodel results is saved in the folder ``Outputs_PostProcessing_calib``, while the accuracy check is given as console output. + +.. container:: twocol + + .. container:: leftside + + .. code-block:: py + + >>>>> Errors of A <<<<< + + Index | RMSE | Validation Error + ----------------------------------- + 1 | 1.513e-07 | 2.224e-15 + + >>>>> Errors of B <<<<< + + Index | RMSE | Validation Error + ----------------------------------- + 1 | 5.045e-05 | 2.406e-11 + + .. container:: rightside + + .. image:: ../../examples/user_guide/Outputs_PostProcessing_calib/Model_vs_PCEModel_y_1.pdf + :width: 400 + :alt: Visual comparison of model and metamodel outputs + \ No newline at end of file diff --git a/docs/build/html/_sources/surrogate_description.rst.txt b/docs/build/html/_sources/surrogate_description.rst.txt index 676b73ba6..3b32fbe2e 100644 --- a/docs/build/html/_sources/surrogate_description.rst.txt +++ b/docs/build/html/_sources/surrogate_description.rst.txt @@ -1,2 +1,98 @@ Training surrogate models -************************* \ No newline at end of file +************************* +Surrogate models, also called metamodels, are models that are built on evaluations of full models with the goal to capture the full behaviour, but reduce the cost of evaluations. + +In BayesValidRox two types of surrogate model are available, polynomial chaos expansion and Gaussian processes. +The Polynomial Chaos Expansion (PCE) and its variant the arbitrary Polynomial Chaos Expansion (aPC) build polynomials from the given distributions of uncertain inputs. +Gaussian processes (GP) give kernel-based representations of the model results. + +The surrogate models are trained on datasets :math:`\mathcal{D}=(x_i, y_i)_{i=1,\dots,M)` that consist of :math:`M` samples of the uncertain parameters and the corresponding model outputs. +We call this dataset the training data, with training samples :math:`(x_i)_{i=1,\dots,M)`. + + +MetaModel and Engine classes +============================ +BayesValidRox creates surrogate models as objects of the class :any:`bayesvalidrox.surrogate_models.surrogate_models.MetaModel`. +Training is performed by the class :any:`bayesvalidrox.surrogate_models.engine.Engine`. + +.. image:: ../diagrams/metamod_training_reduced.png + :width: 800 + :alt: UML diagram for metamodel-related classes in bayesvalidrox + +MetaModel options +================= + + +Training with the engine +======================== +For training a surrogate model we use an object of class :any:`bayesvalidrox.surrogate_models.engine.Engine`. +This needs to be given three things: the metamodel itself, the model that the metamodel should replace and the experimental design that matches the uncertain inputs for the model and metamodel. + +The standard method of training the surrogate is performed by the function ``train_normal()``. +Other available training methods in BayesValidRox are presented in :any:`al_description`. + +For training the engine performs three main steps. + +1) Generating training samples from the experimental design. +2) Evaluating the model on the training samples. +3) Fitting the surrogate to the training dataset. + +Example +======= +We now build a surrogate model for the simple model from :any:`model_description` using the experimental design from :any:`input_description`. +For this we need the classes :any:`bayesvalidrox.surrogate_models.surrogate_models.MetaModel` and :any:`bayesvalidrox.surrogate_models.engine.Engine`. + +>> from bayesvalidrox import MetaModel, Engine + +First we set up the surrogate model and tell it to consider the uncertain parameters defined in ``Inputs`` as its input parameters. + +>>> MetaMod = MetaModel(Inputs) + +Then we specify what type of surrogate we want and its properties. +Here we use an aPCE with maximal polynomial degree 3 and want to use FastARD as the regression method. +We set the value of the q-norm truncation scheme to 0.9. +This combination will give us a sparse aPCE. + +>>> MetaMod.meta_model_type = 'aPCE' +>>> MetaMod.pce_reg_method = 'FastARD' +>>> MetaMod.pce_deg = 3 +>>> MetaMod.pce_q_norm = 0.85 + +Before we start the actual training we need to set some training-related values for the experimental design. +Most importantly we set the attribute ``method`` to 'normal' to indicate that no iterations are performed during the training and we set ``n_init_samples`` to our wanted number of training samples. + +.. warning:: + The attribute ``method`` will be deprecated in further release. + +>>> ExpDesign.method = 'normal' +>>> ExpDesign.n_init_samples = 10 + +Like this the experimental design will generate 10 samples according to our previously set sampling method. +Alternatively we can set the samples that we generated in :any:`input_description` as the training samples. +For this the sampling method should be set to 'user' and our samples given as ``X``. + +>>> ExpDesign.sampling_method = 'user' +>>> ExpDesign.root_samples = samples + +Now we create an engine object with the model, experimental design and surrogate model. +With the function ``start_engine`` the engine performs its preparations for training. + +.. warning:: + The function start_engine will likely be deprecated in future releases. + +>>> Engine_ = Engine(MetaMod, Model, ExpDesign) +>>> Engine_.start_engine() + +Then we train the surrogate model. + +>>> Engine.train_normal() + +We can evaluate the trained surrogate model in two ways, via the engine, or directly. +The evaluations return the mean approximation of the surrogate and its associated standard deviation. +Evaluation via the surrogate model can make use 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given samples and to read in and contain MC references and observations.</p> +<p>Models can be defined via python functions, shell commands or as general executables. +This allows for the use of BayesValidRox with a broad range of models and easy extension to models that are defined with e.g. UM-Bridge.</p> +</div></blockquote> +</div> +<div class="rightside docutils container"> +<a class="reference internal image-reference" href="_images/model.png"><img alt="UML diagram for the bayesvalidrox class :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel`." src="_images/model.png" style="width: 150px;" /></a> +</div> +</div> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Link to this heading">¶</a></h2> +<p>For this example we use a very simple model that maps the uncertain parameter <span class="math notranslate nohighlight">\(X\)</span> from the example in <a class="reference internal" href="input_description.html"><span class="doc">Priors, input space and experimental design</span></a> to two outputs, the original value and its square. +We define this model as a function <code class="docutils literal notranslate"><span class="pre">model</span></code> in a new file <code class="docutils literal notranslate"><span class="pre">model.py</span></code>. +This function takes a single realization of the uncertain parameter as a 2-dimensional <code class="docutils literal notranslate"><span class="pre">np.array</span></code> and returns a dictionary of model results. +Here we use the key <code class="docutils literal notranslate"><span class="pre">A</span></code> for the sample values and <code class="docutils literal notranslate"><span class="pre">B</span></code> for their squares. +Under the key <code class="docutils literal notranslate"><span class="pre">x_values</span></code> a list should be given that is of the same length as each output of the model for a single input. +The values in this list can denote e.g. timesteps and are used in postprocessing as labels of the x-axis.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span> <span class="nf">model</span><span class="p">(</span><span class="n">sample</span><span class="p">):</span> +<span class="gp">>>> </span> <span class="n">square</span> <span class="o">=</span> <span class="n">sample</span><span class="o">*</span><span class="n">sample</span> +<span class="gp">>>> </span> <span class="n">outputs</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'A'</span><span class="p">:</span> <span class="n">sample</span><span class="p">,</span> <span class="s1">'B'</span><span class="p">:</span> <span class="n">square</span><span class="p">,</span> <span class="s1">'x_values'</span><span class="p">:</span> <span class="p">[</span><span class="mi">0</span><span class="p">]}</span> +<span class="gp">>>> </span> <span class="k">return</span> <span class="n">outputs</span> +</pre></div> +</div> +<p>In the main python file we can create an object of <a class="reference internal" href="_autosummary/bayesvalidrox.pylink.pylink.PyLinkForwardModel.html#bayesvalidrox.pylink.pylink.PyLinkForwardModel" title="bayesvalidrox.pylink.pylink.PyLinkForwardModel"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.pylink.pylink.PyLinkForwardModel</span></code></a> that links to this model.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">bayesvalidrox</span> <span class="kn">import</span> <span class="n">PyLinkForwardModel</span> +</pre></div> +</div> +<p>We create an object of this class and set the <code class="docutils literal notranslate"><span class="pre">link_type</span></code> as ‘Function’ to indicate that this is a function in a python file. +<code class="docutils literal notranslate"><span class="pre">py_file</span></code> should be set to the filename of the model and <code class="docutils literal notranslate"><span class="pre">name</span></code> to the name of the function. +Lastly we list the keys of the outputs that we are interested in.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Model</span> <span class="o">=</span> <span class="n">PyLinkForwardModel</span><span class="p">()</span> +<span class="gp">>>> </span><span class="n">Model</span><span class="o">.</span><span class="n">link_type</span> <span class="o">=</span> <span class="s1">'Function'</span> +<span class="gp">>>> </span><span class="n">Model</span><span class="o">.</span><span class="n">py_file</span> <span class="o">=</span> <span class="s1">'model'</span> +<span class="gp">>>> </span><span class="n">Model</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s1">'model'</span> +<span class="gp">>>> </span><span class="n">Model</span><span class="o">.</span><span class="n">Output</span><span class="o">.</span><span class="n">names</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'A'</span><span class="p">,</span> <span class="s1">'B'</span><span class="p">]</span> +</pre></div> +</div> +<p>With this we have completed an interface to our model. +We can now evaluate this model on the samples created in the input example.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">output</span><span class="p">,</span> <span class="n">samples</span> <span class="o">=</span> <span class="n">Model</span><span class="o">.</span><span class="n">run_model_parallel</span><span class="p">(</span><span class="n">samples</span><span class="p">)</span> +</pre></div> +</div> +<p>Other types of model links can be found in <a class="reference internal" href="examples.html"><span class="doc">EXAMPLES</span></a>, e.g. <a class="reference internal" href="beam.html"><span class="doc">Example: beam</span></a> uses a shell command and parser.</p> +</section> +</section> + + </article> + </div> + <footer> + + <div class="related-pages"> + <a class="next-page" href="surrogate_description.html"> + <div class="page-info"> + <div class="context"> + <span>Next</span> + </div> + <div class="title">Training surrogate models</div> + </div> + <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> + </a> + <a class="prev-page" href="input_description.html"> + <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> + <div class="page-info"> + <div class="context"> + <span>Previous</span> + </div> + + <div class="title">Priors, input space and experimental design</div> + + </div> + </a> + </div> + <div class="bottom-of-page"> + <div class="left-details"> + <div class="copyright"> + Copyright 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class="toc-overlay-icon toc-content-icon" for="__toc"> <div class="visually-hidden">Toggle table of contents sidebar</div> <i class="icon"><svg><use href="#svg-toc"></use></svg></i> </label> </div> <article role="main"> - <section id="postprocessing-bayesian-inference-and-bayesian-model-comparison"> -<h1>Postprocessing, Bayesian inference and Bayesian model comparison<a class="headerlink" href="#postprocessing-bayesian-inference-and-bayesian-model-comparison" title="Link to this heading">¶</a></h1> + <section id="postprocessing"> +<h1>Postprocessing<a class="headerlink" href="#postprocessing" title="Link to this heading">¶</a></h1> +<div class="twocol docutils container"> +<div class="leftside docutils container"> +<p>Postprocessing refers to evaluations and checks performed on a model to get an understanding of its properties and estimate its quality. +The BayesValidRox class <a class="reference internal" href="_autosummary/bayesvalidrox.post_processing.post_processing.PostProcessing.html#bayesvalidrox.post_processing.post_processing.PostProcessing" title="bayesvalidrox.post_processing.post_processing.PostProcessing"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.post_processing.post_processing.PostProcessing</span></code></a> includes functions that are applicable to all types of surrogate model.</p> +<blockquote> +<div><ul class="simple"> +<li><p><code class="docutils literal notranslate"><span class="pre">valid_metamodel</span></code>: visualizing some metamodel runs against the corresponding model runs</p></li> +<li><p><code class="docutils literal notranslate"><span class="pre">check_accuracy</span></code>: computing the RMSE error of the surrogate model</p></li> +</ul> +</div></blockquote> +</div> +<div class="rightside docutils container"> +<a class="reference internal image-reference" href="_images/postprocessing.png"><img alt="UML diagram for the classes and functions used in active learning in BayesValidRox." src="_images/postprocessing.png" style="width: 300px;" /></a> +</div> +</div> +<p>Postprocessing methods that are specific to a type of surrogate or training include</p> +<ul class="simple"> +<li><p><code class="docutils literal notranslate"><span class="pre">plot_moments</span></code>: visualizing the moments of a polynomial chaos expansion (PCE, aPCE)</p></li> +<li><p><code class="docutils literal notranslate"><span class="pre">sobol_indices</span></code>: calculating the Sobol’ and Total Sobol’ indices (PCE, aPCE)</p></li> +<li><p><code class="docutils literal notranslate"><span class="pre">plot_seq_design_diagnostics</span></code>: visualizing diagnostics that were evaluated during sequential training (surrogate trained with <code class="docutils literal notranslate"><span class="pre">train_sequential</span></code>)</p></li> +</ul> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Link to this heading">¶</a></h2> +<p>We want to compare out trained surrogate from <a class="reference internal" href="al_description.html"><span class="doc">Active learning: iteratively expanding the training set</span></a> against its original model.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">bayesvalidrox</span> <span class="kn">import</span> <span class="n">PostProcessing</span> +</pre></div> +</div> +<p>The postprocessing object expects the full engine. This allows it to perform both sampling, running the model and running the surrogate model.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">PostProc</span> <span class="o">=</span> <span class="n">PostProcessing</span><span class="p">(</span><span class="n">Engine_</span><span class="p">)</span> +</pre></div> +</div> +<p>To gain an understanding of the approximation quality we use both <code class="docutils literal notranslate"><span class="pre">valid_metamodel</span></code> and <code class="docutils literal notranslate"><span class="pre">check_accuracy</span></code>.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">PostProc</span><span class="o">.</span><span class="n">valid_metamodel</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> +<span class="gp">>>> </span><span class="n">PostProc</span><span class="o">.</span><span class="n">check_accuracy</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span> +</pre></div> +</div> +<p>The visual comparison of model and metamodel results is saved in the folder <code class="docutils literal notranslate"><span class="pre">Outputs_PostProcessing_calib</span></code>, while the accuracy check is given as console output.</p> +<div class="twocol docutils container"> +<div class="leftside docutils container"> +<div class="highlight-py notranslate"><div class="highlight"><pre><span></span><span class="go">>>>>> Errors of A <<<<<</span> + +<span class="go">Index | RMSE | Validation Error</span> +<span class="go">-----------------------------------</span> +<span class="go">1 | 1.513e-07 | 2.224e-15</span> + +<span class="go">>>>>> Errors of B <<<<<</span> + +<span class="go">Index | RMSE | Validation Error</span> +<span class="go">-----------------------------------</span> +<span class="go">1 | 5.045e-05 | 2.406e-11</span> +</pre></div> +</div> +</div> +<div class="rightside docutils container"> +<a class="reference internal image-reference" href="_images/Model_vs_PCEModel_y_1.pdf"><img alt="Visual comparison of model and metamodel outputs" src="_images/Model_vs_PCEModel_y_1.pdf" style="width: 400px;" /></a> +</div> +</div> +</section> </section> </article> @@ -341,23 +402,23 @@ <footer> <div class="related-pages"> - <a class="next-page" href="api.html"> + <a class="next-page" href="bayes_description.html"> <div class="page-info"> <div class="context"> <span>Next</span> </div> - <div class="title">API</div> + <div class="title">Bayesian inference and multi-model comparison</div> </div> <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> </a> - <a class="prev-page" href="surrogate_description.html"> + <a class="prev-page" 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id="training-surrogate-models"> <h1>Training surrogate models<a class="headerlink" href="#training-surrogate-models" title="Link to this heading">¶</a></h1> +<p>Surrogate models, also called metamodels, are models that are built on evaluations of full models with the goal to capture the full behaviour, but reduce the cost of evaluations.</p> +<p>In BayesValidRox two types of surrogate model are available, polynomial chaos expansion and Gaussian processes. +The Polynomial Chaos Expansion (PCE) and its variant the arbitrary Polynomial Chaos Expansion (aPC) build polynomials from the given distributions of uncertain inputs. +Gaussian processes (GP) give kernel-based representations of the model results.</p> +<p>The surrogate models are trained on datasets <span class="math notranslate nohighlight">\(\mathcal{D}=(x_i, y_i)_{i=1,\dots,M)\)</span> that consist of <span class="math notranslate nohighlight">\(M\)</span> samples of the uncertain parameters and the corresponding model outputs. +We call this dataset the training data, with training samples <span class="math notranslate nohighlight">\((x_i)_{i=1,\dots,M)\)</span>.</p> +<section id="metamodel-and-engine-classes"> +<h2>MetaModel and Engine classes<a class="headerlink" href="#metamodel-and-engine-classes" title="Link to this heading">¶</a></h2> +<p>BayesValidRox creates surrogate models as objects of the class <a class="reference internal" href="_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html#bayesvalidrox.surrogate_models.surrogate_models.MetaModel" title="bayesvalidrox.surrogate_models.surrogate_models.MetaModel"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.surrogate_models.surrogate_models.MetaModel</span></code></a>. +Training is performed by the class <a class="reference internal" href="_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html#bayesvalidrox.surrogate_models.engine.Engine" title="bayesvalidrox.surrogate_models.engine.Engine"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.surrogate_models.engine.Engine</span></code></a>.</p> +<a class="reference internal image-reference" href="_images/metamod_training_reduced.png"><img alt="UML diagram for metamodel-related classes in bayesvalidrox" src="_images/metamod_training_reduced.png" style="width: 800px;" /></a> +</section> +<section id="metamodel-options"> +<h2>MetaModel options<a class="headerlink" href="#metamodel-options" title="Link to this heading">¶</a></h2> +</section> +<section id="training-with-the-engine"> +<h2>Training with the engine<a class="headerlink" href="#training-with-the-engine" title="Link to this heading">¶</a></h2> +<p>For training a surrogate model we use an object of class <a class="reference internal" href="_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html#bayesvalidrox.surrogate_models.engine.Engine" title="bayesvalidrox.surrogate_models.engine.Engine"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.surrogate_models.engine.Engine</span></code></a>. +This needs to be given three things: the metamodel itself, the model that the metamodel should replace and the experimental design that matches the uncertain inputs for the model and metamodel.</p> +<p>The standard method of training the surrogate is performed by the function <code class="docutils literal notranslate"><span class="pre">train_normal()</span></code>. +Other available training methods in BayesValidRox are presented in <a class="reference internal" href="al_description.html"><span class="doc">Active learning: iteratively expanding the training set</span></a>.</p> +<p>For training the engine performs three main steps.</p> +<ol class="arabic simple"> +<li><p>Generating training samples from the experimental design.</p></li> +<li><p>Evaluating the model on the training samples.</p></li> +<li><p>Fitting the surrogate to the training dataset.</p></li> +</ol> +</section> +<section id="example"> +<h2>Example<a class="headerlink" href="#example" title="Link to this heading">¶</a></h2> +<p>We now build a surrogate model for the simple model from <a class="reference internal" href="model_description.html"><span class="doc">Models</span></a> using the experimental design from <a class="reference internal" href="input_description.html"><span class="doc">Priors, input space and experimental design</span></a>. +For this we need the classes <a class="reference internal" href="_autosummary/bayesvalidrox.surrogate_models.surrogate_models.MetaModel.html#bayesvalidrox.surrogate_models.surrogate_models.MetaModel" title="bayesvalidrox.surrogate_models.surrogate_models.MetaModel"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.surrogate_models.surrogate_models.MetaModel</span></code></a> and <a class="reference internal" href="_autosummary/bayesvalidrox.surrogate_models.engine.Engine.html#bayesvalidrox.surrogate_models.engine.Engine" title="bayesvalidrox.surrogate_models.engine.Engine"><code class="xref any py py-class docutils literal notranslate"><span class="pre">bayesvalidrox.surrogate_models.engine.Engine</span></code></a>.</p> +<p>>> from bayesvalidrox import MetaModel, Engine</p> +<p>First we set up the surrogate model and tell it to consider the uncertain parameters defined in <code class="docutils literal notranslate"><span class="pre">Inputs</span></code> as its input parameters.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">MetaMod</span> <span class="o">=</span> <span class="n">MetaModel</span><span class="p">(</span><span class="n">Inputs</span><span class="p">)</span> +</pre></div> +</div> +<p>Then we specify what type of surrogate we want and its properties. +Here we use an aPCE with maximal polynomial degree 3 and want to use FastARD as the regression method. +We set the value of the q-norm truncation scheme to 0.9. +This combination will give us a sparse aPCE.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">MetaMod</span><span class="o">.</span><span class="n">meta_model_type</span> <span class="o">=</span> <span class="s1">'aPCE'</span> +<span class="gp">>>> </span><span class="n">MetaMod</span><span class="o">.</span><span class="n">pce_reg_method</span> <span class="o">=</span> <span class="s1">'FastARD'</span> +<span class="gp">>>> </span><span class="n">MetaMod</span><span class="o">.</span><span class="n">pce_deg</span> <span class="o">=</span> <span class="mi">3</span> +<span class="gp">>>> </span><span class="n">MetaMod</span><span class="o">.</span><span class="n">pce_q_norm</span> <span class="o">=</span> <span class="mf">0.85</span> +</pre></div> +</div> +<p>Before we start the actual training we need to set some training-related values for the experimental design. +Most importantly we set the attribute <code class="docutils literal notranslate"><span class="pre">method</span></code> to ‘normal’ to indicate that no iterations are performed during the training and we set <code class="docutils literal notranslate"><span class="pre">n_init_samples</span></code> to our wanted number of training samples.</p> +<div class="admonition warning"> +<p class="admonition-title">Warning</p> +<p>The attribute <code class="docutils literal notranslate"><span class="pre">method</span></code> will be deprecated in further release.</p> +</div> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">ExpDesign</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'normal'</span> +<span class="gp">>>> </span><span class="n">ExpDesign</span><span class="o">.</span><span class="n">n_init_samples</span> <span class="o">=</span> <span class="mi">10</span> +</pre></div> +</div> +<p>Like this the experimental design will generate 10 samples according to our previously set sampling method. +Alternatively we can set the samples that we generated in <a class="reference internal" href="input_description.html"><span class="doc">Priors, input space and experimental design</span></a> as the training samples. +For this the sampling method should be set to ‘user’ and our samples given as <code class="docutils literal notranslate"><span class="pre">X</span></code>.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">ExpDesign</span><span class="o">.</span><span class="n">sampling_method</span> <span class="o">=</span> <span class="s1">'user'</span> +<span class="gp">>>> </span><span class="n">ExpDesign</span><span class="o">.</span><span class="n">root_samples</span> <span class="o">=</span> <span class="n">samples</span> +</pre></div> +</div> +<p>Now we create an engine object with the model, experimental design and surrogate model. +With the function <code class="docutils literal notranslate"><span class="pre">start_engine</span></code> the engine performs its preparations for training.</p> +<div class="admonition warning"> +<p class="admonition-title">Warning</p> +<p>The function start_engine will likely be deprecated in future releases.</p> +</div> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Engine_</span> <span class="o">=</span> <span class="n">Engine</span><span class="p">(</span><span class="n">MetaMod</span><span class="p">,</span> <span class="n">Model</span><span class="p">,</span> <span class="n">ExpDesign</span><span class="p">)</span> +<span class="gp">>>> </span><span class="n">Engine_</span><span class="o">.</span><span class="n">start_engine</span><span class="p">()</span> +</pre></div> +</div> +<p>Then we train the surrogate model.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">Engine</span><span class="o">.</span><span class="n">train_normal</span><span class="p">()</span> +</pre></div> +</div> +<p>We can evaluate the trained surrogate model in two ways, via the engine, or directly. +The evaluations return the mean approximation of the surrogate and its associated standard deviation. +Evaluation via the surrogate model can make use of the sampling in the experimental design,</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">mean</span><span class="p">,</span> <span class="n">stdev</span> <span class="o">=</span> <span class="n">Engine_</span><span class="o">.</span><span class="n">eval_metamodel</span><span class="p">(</span><span class="n">nsamples</span> <span class="o">=</span> <span class="mi">10</span><span class="p">)</span> +</pre></div> +</div> +<p>while for direct evaluation the exact set of samples has to be given.</p> +<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">mean</span><span class="p">,</span> <span class="n">stdev</span> <span class="o">=</span> <span class="n">Engine_</span><span class="o">.</span><span class="n">MetaModel</span><span class="o">.</span><span class="n">eval_metamodel</span><span class="p">(</span><span class="n">samples</span><span class="p">)</span> +</pre></div> +</div> +</section> </section> </article> @@ -341,23 +432,23 @@ <footer> <div class="related-pages"> - <a class="next-page" href="post_description.html"> + <a class="next-page" href="al_description.html"> <div class="page-info"> <div class="context"> <span>Next</span> </div> - <div class="title">Postprocessing, Bayesian inference and Bayesian model comparison</div> + <div class="title">Active learning: iteratively expanding the training set</div> </div> <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> </a> - <a class="prev-page" href="input_description.html"> + <a class="prev-page" href="model_description.html"> <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> <div class="page-info"> <div class="context"> <span>Previous</span> </div> - <div class="title">Priors, input space and experimental design</div> + <div class="title">Models</div> </div> </a> @@ -379,9 +470,31 @@ </footer> </div> - <aside class="toc-drawer no-toc"> + <aside class="toc-drawer"> + <div class="toc-sticky toc-scroll"> + <div class="toc-title-container"> + <span class="toc-title"> + On this page + </span> + </div> + <div class="toc-tree-container"> + <div class="toc-tree"> + <ul> +<li><a class="reference internal" href="#">Training surrogate models</a><ul> +<li><a class="reference internal" href="#metamodel-and-engine-classes">MetaModel and Engine classes</a></li> +<li><a class="reference internal" href="#metamodel-options">MetaModel options</a></li> +<li><a class="reference internal" href="#training-with-the-engine">Training with the engine</a></li> +<li><a class="reference internal" href="#example">Example</a></li> +</ul> +</li> +</ul> + + </div> + </div> + </div> + </aside> </div> @@ -389,5 +502,6 @@ <script src="_static/doctools.js?v=9a2dae69"></script> <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/scripts/furo.js?v=32e29ea5"></script> + <script async="async" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js"></script> </body> </html> \ No newline at end of file diff --git a/docs/build/html/tutorial.html b/docs/build/html/tutorial.html index 377714039..2cf29844b 100644 --- a/docs/build/html/tutorial.html +++ b/docs/build/html/tutorial.html @@ -3,7 +3,7 @@ <head><meta charset="utf-8"/> <meta name="viewport" content="width=device-width,initial-scale=1"/> <meta name="color-scheme" content="light dark"><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> -<link rel="index" title="Index" href="genindex.html" /><link rel="search" title="Search" href="search.html" /><link rel="next" title="EXAMPLES" href="examples.html" /><link rel="prev" title="Surrogate-assisted Bayesian validation of computational models" href="index.html" /> +<link rel="index" title="Index" href="genindex.html" /><link rel="search" title="Search" href="search.html" /><link rel="next" title="EXAMPLES" href="examples.html" /><link rel="prev" title="Postprocessing, Bayesian inference and Bayesian model comparison" href="post_description.html" /> <!-- Generated with Sphinx 7.3.7 and Furo 2023.09.10 --> <title>TUTORIAL - bayesvalidrox 1.0.0 documentation</title> @@ -164,8 +164,14 @@ </form> <div id="searchbox"></div><div class="sidebar-scroll"><div class="sidebar-tree"> <ul class="current"> +<li class="toctree-l1 has-children"><a class="reference internal" href="packagedescription.html">USER GUIDE</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" role="switch" type="checkbox"/><label for="toctree-checkbox-1"><div class="visually-hidden">Toggle navigation of USER GUIDE</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul> +<li class="toctree-l2"><a class="reference internal" href="input_description.html">Priors, input space and experimental design</a></li> +<li class="toctree-l2"><a class="reference internal" href="surrogate_description.html">Training surrogate models</a></li> +<li class="toctree-l2"><a class="reference internal" href="post_description.html">Postprocessing, Bayesian inference and Bayesian model comparison</a></li> +</ul> +</li> <li class="toctree-l1 current current-page"><a class="current 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href="post_description.html">Postprocessing, Bayesian inference and Bayesian model comparison</a></li> -</ul> -</li> <li class="toctree-l1 has-children"><a class="reference internal" href="api.html">API</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" role="switch" type="checkbox"/><label for="toctree-checkbox-3"><div class="visually-hidden">Toggle navigation of API</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul> <li class="toctree-l2 has-children"><a class="reference internal" href="_autosummary/bayesvalidrox.html">bayesvalidrox</a><input class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" role="switch" type="checkbox"/><label for="toctree-checkbox-4"><div class="visually-hidden">Toggle navigation of bayesvalidrox</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul> <li class="toctree-l3 has-children"><a class="reference internal" href="_autosummary/bayesvalidrox.bayes_inference.html">bayesvalidrox.bayes_inference</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" role="switch" type="checkbox"/><label for="toctree-checkbox-5"><div class="visually-hidden">Toggle navigation of bayesvalidrox.bayes_inference</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul> @@ -698,14 +698,14 @@ plots of posterior predictions if wanted.</p> </div> <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> </a> - <a class="prev-page" href="index.html"> + <a class="prev-page" href="post_description.html"> <svg class="furo-related-icon"><use href="#svg-arrow-right"></use></svg> <div class="page-info"> <div class="context"> <span>Previous</span> </div> - <div class="title">Home</div> + <div class="title">Postprocessing, Bayesian inference and Bayesian model comparison</div> </div> </a> diff --git a/docs/source/al_description.rst b/docs/source/al_description.rst new file mode 100644 index 000000000..636fa7877 --- /dev/null +++ b/docs/source/al_description.rst @@ -0,0 +1,8 @@ +Active learning: iteratively expanding the training set +******************************************************* + + + +.. image:: ../diagrams/active_learning_reduced.png + :width: 550 + :alt: UML diagram for the classes and functions used in active learning in BayesValidRox. \ No newline at end of file diff --git a/docs/source/bayes_description.rst b/docs/source/bayes_description.rst new file mode 100644 index 000000000..2cfd3a6a8 --- /dev/null +++ b/docs/source/bayes_description.rst @@ -0,0 +1,7 @@ +Bayesian inference and multi-model comparison +********************************************* + + +.. image:: ../diagrams/bayesian_validation.png + :width: 300 + :alt: UML diagram for classes related to Bayesian inference and multi-model comparison. diff --git a/docs/source/conf.py b/docs/source/conf.py index 7b710d360..fc4af8322 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -36,7 +36,8 @@ extensions = [ 'sphinx.ext.doctest', 'sphinx.ext.autodoc', 'sphinx.ext.autosummary', - 'm2r2' + 'm2r2', + 'sphinx.ext.mathjax', ] # Add any paths that contain templates here, relative to this directory. @@ -47,6 +48,9 @@ templates_path = ['_templates'] # This pattern also affects html_static_path and html_extra_path. exclude_patterns = [] +# Path for mathjax +mathjax_path = 'http://cdn.mathjax.org/mathjax/latest/MathJax.js' + # -- Options for HTML output ------------------------------------------------- diff --git a/docs/source/model_description.rst b/docs/source/model_description.rst new file mode 100644 index 000000000..f08ea0cd2 --- /dev/null +++ b/docs/source/model_description.rst @@ -0,0 +1,54 @@ +Models +****** + +.. container:: twocol + + .. container:: leftside + + BayesValidRox gives options to create interfaces for a variety of models with the class :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel`. + + Its main function is to run the model on given samples and to read in and contain MC references and observations. + + Models can be defined via python functions, shell commands or as general executables. + This allows for the use of BayesValidRox with a broad range of models and easy extension to models that are defined with e.g. UM-Bridge. + + .. container:: rightside + + .. image:: ../diagrams/model.png + :width: 150 + :alt: UML diagram for the bayesvalidrox class :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel`. + +Example +======= +For this example we use a very simple model that maps the uncertain parameter :math:`X` from the example in :any:`input_description` to two outputs, the original value and its square. +We define this model as a function ``model`` in a new file ``model.py``. +This function takes a single realization of the uncertain parameter as a 2-dimensional ``np.array`` and returns a dictionary of model results. +Here we use the key ``A`` for the sample values and ``B`` for their squares. +Under the key ``x_values`` a list should be given that is of the same length as each output of the model for a single input. +The values in this list can denote e.g. timesteps and are used in postprocessing as labels of the x-axis. + +>>> def model(sample): +>>> square = sample*sample +>>> outputs = {'A': sample, 'B': square, 'x_values': [0]} +>>> return outputs + +In the main python file we can create an object of :any:`bayesvalidrox.pylink.pylink.PyLinkForwardModel` that links to this model. + +>>> from bayesvalidrox import PyLinkForwardModel + +We create an object of this class and set the ``link_type`` as 'Function' to indicate that this is a function in a python file. +``py_file`` should be set to the filename of the model and ``name`` to the name of the function. +Lastly we list the keys of the outputs that we are interested in. + +>>> Model = PyLinkForwardModel() +>>> Model.link_type = 'Function' +>>> Model.py_file = 'model' +>>> Model.name = 'model' +>>> Model.Output.names = ['A', 'B'] + +With this we have completed an interface to our model. +We can now evaluate this model on the samples created in the input example. + +>>> output, samples = Model.run_model_parallel(samples) + +Other types of model links can be found in :any:`examples`, e.g. :any:`beam` uses a shell command and parser. diff --git a/docs/source/post_description.rst b/docs/source/post_description.rst index 9950c8cf9..af2172709 100644 --- a/docs/source/post_description.rst +++ b/docs/source/post_description.rst @@ -1,2 +1,66 @@ -Postprocessing, Bayesian inference and Bayesian model comparison -**************************************************************** \ No newline at end of file +Postprocessing +************** +.. container:: twocol + + .. container:: leftside + + Postprocessing refers to evaluations and checks performed on a model to get an understanding of its properties and estimate its quality. + The BayesValidRox class :any:`bayesvalidrox.post_processing.post_processing.PostProcessing` includes functions that are applicable to all types of surrogate model. + + * ``valid_metamodel``: visualizing some metamodel runs against the corresponding model runs + * ``check_accuracy``: computing the RMSE error of the surrogate model + + .. container:: rightside + + .. image:: ../diagrams/postprocessing.png + :width: 300 + :alt: UML diagram for the classes and functions used in active learning in BayesValidRox. + +Postprocessing methods that are specific to a type of surrogate or training include + +* ``plot_moments``: visualizing the moments of a polynomial chaos expansion (PCE, aPCE) +* ``sobol_indices``: calculating the Sobol' and Total Sobol' indices (PCE, aPCE) +* ``plot_seq_design_diagnostics``: visualizing diagnostics that were evaluated during sequential training (surrogate trained with ``train_sequential``) + + +Example +======= +We want to compare out trained surrogate from :any:`al_description` against its original model. + +>>> from bayesvalidrox import PostProcessing + +The postprocessing object expects the full engine. This allows it to perform both sampling, running the model and running the surrogate model. + +>>> PostProc = PostProcessing(Engine_) + +To gain an understanding of the approximation quality we use both ``valid_metamodel`` and ``check_accuracy``. + +>>> PostProc.valid_metamodel(n_samples=1) +>>> PostProc.check_accuracy(n_samples=10) + +The visual comparison of model and metamodel results is saved in the folder ``Outputs_PostProcessing_calib``, while the accuracy check is given as console output. + +.. container:: twocol + + .. container:: leftside + + .. code-block:: py + + >>>>> Errors of A <<<<< + + Index | RMSE | Validation Error + ----------------------------------- + 1 | 1.513e-07 | 2.224e-15 + + >>>>> Errors of B <<<<< + + Index | RMSE | Validation Error + ----------------------------------- + 1 | 5.045e-05 | 2.406e-11 + + .. container:: rightside + + .. image:: ../../examples/user_guide/Outputs_PostProcessing_calib/Model_vs_PCEModel_y_1.pdf + :width: 400 + :alt: Visual comparison of model and metamodel outputs + \ No newline at end of file diff --git a/docs/source/surrogate_description.rst b/docs/source/surrogate_description.rst index 676b73ba6..3b32fbe2e 100644 --- a/docs/source/surrogate_description.rst +++ b/docs/source/surrogate_description.rst @@ -1,2 +1,98 @@ Training surrogate models -************************* \ No newline at end of file +************************* +Surrogate models, also called metamodels, are models that are built on evaluations of full models with the goal to capture the full behaviour, but reduce the cost of evaluations. + +In BayesValidRox two types of surrogate model are available, polynomial chaos expansion and Gaussian processes. +The Polynomial Chaos Expansion (PCE) and its variant the arbitrary Polynomial Chaos Expansion (aPC) build polynomials from the given distributions of uncertain inputs. +Gaussian processes (GP) give kernel-based representations of the model results. + +The surrogate models are trained on datasets :math:`\mathcal{D}=(x_i, y_i)_{i=1,\dots,M)` that consist of :math:`M` samples of the uncertain parameters and the corresponding model outputs. +We call this dataset the training data, with training samples :math:`(x_i)_{i=1,\dots,M)`. + + +MetaModel and Engine classes +============================ +BayesValidRox creates surrogate models as objects of the class :any:`bayesvalidrox.surrogate_models.surrogate_models.MetaModel`. +Training is performed by the class :any:`bayesvalidrox.surrogate_models.engine.Engine`. + +.. image:: ../diagrams/metamod_training_reduced.png + :width: 800 + :alt: UML diagram for metamodel-related classes in bayesvalidrox + +MetaModel options +================= + + +Training with the engine +======================== +For training a surrogate model we use an object of class :any:`bayesvalidrox.surrogate_models.engine.Engine`. +This needs to be given three things: the metamodel itself, the model that the metamodel should replace and the experimental design that matches the uncertain inputs for the model and metamodel. + +The standard method of training the surrogate is performed by the function ``train_normal()``. +Other available training methods in BayesValidRox are presented in :any:`al_description`. + +For training the engine performs three main steps. + +1) Generating training samples from the experimental design. +2) Evaluating the model on the training samples. +3) Fitting the surrogate to the training dataset. + +Example +======= +We now build a surrogate model for the simple model from :any:`model_description` using the experimental design from :any:`input_description`. +For this we need the classes :any:`bayesvalidrox.surrogate_models.surrogate_models.MetaModel` and :any:`bayesvalidrox.surrogate_models.engine.Engine`. + +>> from bayesvalidrox import MetaModel, Engine + +First we set up the surrogate model and tell it to consider the uncertain parameters defined in ``Inputs`` as its input parameters. + +>>> MetaMod = MetaModel(Inputs) + +Then we specify what type of surrogate we want and its properties. +Here we use an aPCE with maximal polynomial degree 3 and want to use FastARD as the regression method. +We set the value of the q-norm truncation scheme to 0.9. +This combination will give us a sparse aPCE. + +>>> MetaMod.meta_model_type = 'aPCE' +>>> MetaMod.pce_reg_method = 'FastARD' +>>> MetaMod.pce_deg = 3 +>>> MetaMod.pce_q_norm = 0.85 + +Before we start the actual training we need to set some training-related values for the experimental design. +Most importantly we set the attribute ``method`` to 'normal' to indicate that no iterations are performed during the training and we set ``n_init_samples`` to our wanted number of training samples. + +.. warning:: + The attribute ``method`` will be deprecated in further release. + +>>> ExpDesign.method = 'normal' +>>> ExpDesign.n_init_samples = 10 + +Like this the experimental design will generate 10 samples according to our previously set sampling method. +Alternatively we can set the samples that we generated in :any:`input_description` as the training samples. +For this the sampling method should be set to 'user' and our samples given as ``X``. + +>>> ExpDesign.sampling_method = 'user' +>>> ExpDesign.root_samples = samples + +Now we create an engine object with the model, experimental design and surrogate model. +With the function ``start_engine`` the engine performs its preparations for training. + +.. warning:: + The function start_engine will likely be deprecated in future releases. + +>>> Engine_ = Engine(MetaMod, Model, ExpDesign) +>>> Engine_.start_engine() + +Then we train the surrogate model. + +>>> Engine.train_normal() + +We can evaluate the trained surrogate model in two ways, via the engine, or directly. +The evaluations return the mean approximation of the surrogate and its associated standard deviation. +Evaluation via the surrogate model can make use of the sampling in the experimental design, + +>>> mean, stdev = Engine_.eval_metamodel(nsamples = 10) + +while for direct evaluation the exact set of samples has to be given. + +>>> mean, stdev = Engine_.MetaModel.eval_metamodel(samples) diff --git a/examples/user_guide/model.py b/examples/user_guide/model.py new file mode 100644 index 000000000..2bb1b011f --- /dev/null +++ b/examples/user_guide/model.py @@ -0,0 +1,13 @@ +# -*- coding: utf-8 -*- +""" +A simple model example for the BVR user guide. + +@author: Rebecca Kohlhaas +""" +import numpy as np + +def model(samples): + samples = samples[0] + square = np.power(samples, 2) + outputs = {'A': samples, 'B': square, 'x_values': [0]} + return outputs \ No newline at end of file -- GitLab