:orphan:

.. _Surrogate modeling:

Surrogate modeling
==================



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. thumbnail-parent-div-close

.. raw:: html

    </div>


Linear regression
-----------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Export a metamodel">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_export_metamodel_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_export_metamodel`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Export a metamodel</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a linear least squares model">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_create_linear_least_squares_model_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_create_linear_least_squares_model`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a linear least squares model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a general linear model metamodel">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_gaussian_process_fitter_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_gaussian_process_fitter`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a general linear model metamodel</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Taylor approximations">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_taylor_approximation_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_taylor_approximation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Taylor approximations</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a linear model">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_linear_model_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_linear_model`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a linear model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Mixture of experts">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_expert_mixture_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_expert_mixture`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Mixture of experts</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="We consider te so-called Linthurst data set, which contains measures of aerial biomass (BIO) as well as 5 five physicochemical properties of the soil: salinity (SAL), pH, K, Na, and Zn.">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_stepwise_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_stepwise`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Perform stepwise regression</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Distribution of estimators in linear regression">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_distribution_linear_regression_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_distribution_linear_regression`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Distribution of estimators in linear regression</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Over-fitting and model selection">

.. only:: html

  .. image:: /auto_surrogate_modeling/linear_regression/images/thumb/sphx_glr_plot_overfitting_model_selection_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/linear_regression/plot_overfitting_model_selection`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Over-fitting and model selection</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Polynomial chaos
----------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Apply a transform or inverse transform on your polynomial chaos">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_distribution_transformation_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_distribution_transformation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Apply a transform or inverse transform on your polynomial chaos</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Fit a distribution from an input sample">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_build_distribution_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_build_distribution`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Fit a distribution from an input sample</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The goal of this example is to create a polynomial chaos expansion using the FunctionalChaosAlgorithm class and see the different methods of the FunctionalChaosResult class. In order to understand the different results, let us review some notations associated to the polynomial chaos expansion.">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_exploitation_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_exploitation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Polynomial chaos exploitation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Get the (output) marginal of a PCE">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_getmarginal_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_getmarginal`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Get the (output) marginal of a PCE</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Compute grouped indices for the Ishigami function">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_ishigami_grouped_indices_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_ishigami_grouped_indices`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Compute grouped indices for the Ishigami function</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Polynomial chaos graphs">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_graphs_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_graphs`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Polynomial chaos graphs</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Validate a polynomial chaos">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_draw_validation_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_draw_validation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Validate a polynomial chaos</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a full or sparse polynomial chaos expansion">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_database_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_database`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a full or sparse polynomial chaos expansion</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a polynomial chaos metamodel by integration on the cantilever beam">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_cantilever_beam_integration_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_cantilever_beam_integration`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a polynomial chaos metamodel by integration on the cantilever beam</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Advanced polynomial chaos construction">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_advanced_ctors_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_advanced_ctors`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Advanced polynomial chaos construction</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a polynomial chaos metamodel from a data set">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_functional_chaos_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a polynomial chaos metamodel from a data set</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_ishigami_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_ishigami`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Plot enumeration rules">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_enumeratefunction_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_enumeratefunction`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Plot enumeration rules</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Pitfalls in  polynomial chaos expansion due to the input distribution">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_lognormal_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_lognormal`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pitfalls in  polynomial chaos expansion due to the input distribution</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Polynomial chaos is sensitive to the degree">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_beam_sensitivity_degree_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_beam_sensitivity_degree`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Polynomial chaos is sensitive to the degree</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Create a sparse chaos by integration">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_cleaning_strategy_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_cleaning_strategy`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Create a sparse chaos by integration</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Compute Sobol&#x27; indices confidence intervals">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_sobol_confidence_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_sobol_confidence`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Compute Sobol' indices confidence intervals</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Conditional expectation of a polynomial chaos expansion">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_conditional_expectation_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_conditional_expectation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Conditional expectation of a polynomial chaos expansion</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Polynomial chaos expansion cross-validation">

.. only:: html

  .. image:: /auto_surrogate_modeling/polynomial_chaos/images/thumb/sphx_glr_plot_chaos_cv_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/polynomial_chaos/plot_chaos_cv`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Polynomial chaos expansion cross-validation</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Gaussian Process Regression
---------------------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian process regression: draw the likelihood">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_likelihood_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_likelihood`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian process regression: draw the likelihood</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example we propagate uncertainties through a GP metamodel of the Ishigami model&lt;use-case-ishigami&gt;.">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_propagate_gpr_ishigami_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_propagate_gpr_ishigami`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: propagate uncertainties</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: multiple input dimensions">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: multiple input dimensions</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression : cantilever beam model">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_cantilever_beam_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_cantilever_beam`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression : cantilever beam model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Multi-output Gaussian Process Regression on the fire satellite model">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_kriging_multioutput_firesatellite_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_kriging_multioutput_firesatellite`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Multi-output Gaussian Process Regression on the fire satellite model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: choose an arbitrary trend">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_beam_arbitrary_trend_thumb.png
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_beam_arbitrary_trend`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: choose an arbitrary trend</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: choose a polynomial trend on the beam model">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_beam_trend_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_beam_trend`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: choose a polynomial trend on the beam model</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression : generate trajectories from the metamodel">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_simulate_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_simulate`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression : generate trajectories from the metamodel</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: Normalization for optimization">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_normalization_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_normalization`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: Normalization for optimization</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In typical machine learning applications, Gaussian process regression surrogate models take several inputs, and those inputs are usually heterogeneous (e.g. in the cantilever beam &lt;/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_cantilever_beam&gt; use case, inputs are various physical quantities).">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_isotropic_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_isotropic`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: use an isotropic covariance kernel</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: metamodel of the Branin-Hoo function">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_kriging_branin_function_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_kriging_branin_function`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: metamodel of the Branin-Hoo function</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression : quick-start">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_1d_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_1d`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression : quick-start</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Sequentially adding new points to a Gaussian Process metamodel">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_kriging_sequential_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_kriging_sequential`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Sequentially adding new points to a Gaussian Process metamodel</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian process fitter: configure the optimization solver">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_hyperparameters_optimization_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_hyperparameters_optimization`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian process fitter: configure the optimization solver</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process-based active learning for reliability">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_active_learning_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_active_learning`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process-based active learning for reliability</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Advanced Gaussian process regression">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_advanced_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_advanced`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Advanced Gaussian process regression</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Kriging : draw covariance models">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_draw_covariance_models_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_draw_covariance_models`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Kriging : draw covariance models</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: choose a polynomial trend">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_choose_trend_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_choose_trend`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: choose a polynomial trend</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Gaussian Process Regression: surrogate model with continuous and categorical variables">

.. only:: html

  .. image:: /auto_surrogate_modeling/gaussian_process_regression/images/thumb/sphx_glr_plot_gpr_categorical_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/gaussian_process_regression/plot_gpr_categorical`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gaussian Process Regression: surrogate model with continuous and categorical variables</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


Fields surrogate models
-----------------------



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Validation of a Karhunen-Loeve decomposition">

.. only:: html

  .. image:: /auto_surrogate_modeling/fields_surrogate_models/images/thumb/sphx_glr_plot_karhunenloeve_validation_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/fields_surrogate_models/plot_karhunenloeve_validation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Validation of a Karhunen-Loeve decomposition</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Viscous free fall: metamodel of a field function">

.. only:: html

  .. image:: /auto_surrogate_modeling/fields_surrogate_models/images/thumb/sphx_glr_plot_viscous_fall_metamodel_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/fields_surrogate_models/plot_viscous_fall_metamodel`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Viscous free fall: metamodel of a field function</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Metamodel of a field function">

.. only:: html

  .. image:: /auto_surrogate_modeling/fields_surrogate_models/images/thumb/sphx_glr_plot_fieldfunction_metamodel_thumb.svg
    :alt:

  :doc:`/auto_surrogate_modeling/fields_surrogate_models/plot_fieldfunction_metamodel`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Metamodel of a field function</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_surrogate_modeling/linear_regression/index.rst
   /auto_surrogate_modeling/polynomial_chaos/index.rst
   /auto_surrogate_modeling/gaussian_process_regression/index.rst
   /auto_surrogate_modeling/fields_surrogate_models/index.rst