.. _sphx_glr_auto_surrogate_modeling_gaussian_process_regression:

.. _gaussian_process_regression_examples:

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



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

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

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  .. 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`

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


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    <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;.">

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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    <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).">

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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      <div class="sphx-glr-thumbnail-title">Advanced Gaussian process regression</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Kriging : draw covariance models">

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  .. 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`

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


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

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  .. 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`

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


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

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  .. 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`

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


.. toctree::
   :hidden:

   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_likelihood
   /auto_surrogate_modeling/gaussian_process_regression/plot_propagate_gpr_ishigami
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_cantilever_beam
   /auto_surrogate_modeling/gaussian_process_regression/plot_kriging_multioutput_firesatellite
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_beam_arbitrary_trend
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_beam_trend
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_simulate
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_normalization
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_isotropic
   /auto_surrogate_modeling/gaussian_process_regression/plot_kriging_branin_function
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_1d
   /auto_surrogate_modeling/gaussian_process_regression/plot_kriging_sequential
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_hyperparameters_optimization
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_active_learning
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_advanced
   /auto_surrogate_modeling/gaussian_process_regression/plot_draw_covariance_models
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_choose_trend
   /auto_surrogate_modeling/gaussian_process_regression/plot_gpr_categorical