.. _sphx_glr_auto_surrogate_modeling_polynomial_chaos:

.. _Polynomial chaos:

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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_distribution_transformation.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_build_distribution.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos_exploitation.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos_getmarginal.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_ishigami_grouped_indices.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos_graphs.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_draw_validation.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos_database.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_cantilever_beam_integration.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos_advanced_ctors.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_functional_chaos.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_ishigami.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_enumeratefunction.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_lognormal.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_beam_sensitivity_degree.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_cleaning_strategy.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_sobol_confidence.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_conditional_expectation.py`

.. 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:

  :ref:`sphx_glr_auto_surrogate_modeling_polynomial_chaos_plot_chaos_cv.py`

.. raw:: html

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


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_distribution_transformation
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_build_distribution
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_exploitation
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_getmarginal
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_ishigami_grouped_indices
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_graphs
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_draw_validation
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_database
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_cantilever_beam_integration
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos_advanced_ctors
   /auto_surrogate_modeling/polynomial_chaos/plot_functional_chaos
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_ishigami
   /auto_surrogate_modeling/polynomial_chaos/plot_enumeratefunction
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_lognormal
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_beam_sensitivity_degree
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_cleaning_strategy
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_sobol_confidence
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_conditional_expectation
   /auto_surrogate_modeling/polynomial_chaos/plot_chaos_cv