:orphan:

Generalized Polynomial Chaos
----------------------------




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    <div class="sphx-glr-thumbcontainer" tooltip="The probability density function (pdf) p_i(\xi_i), with i=1,...,d, has to be defined for each r...">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_problem_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_problem.py`

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      <div class="sphx-glr-thumbnail-title">How to define a gPC problem</div>
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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_gpc_validation_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_gpc_validation.py`

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      <div class="sphx-glr-thumbnail-title">Validation of gPC approximation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Introduction ^^^^^^^^^^^^ A large number of models show redundancies in the form of correlation...">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_projection_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_projection.py`

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      <div class="sphx-glr-thumbnail-title">Dimensionality reduction</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In some cases, the output quantities of a model are discontinuous in the investigated parameter...">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_multi_element_gpc_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_multi_element_gpc.py`

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      <div class="sphx-glr-thumbnail-title">Modelling discontinuous model functions</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Setting up a custom model">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_model_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_model.py`

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      <div class="sphx-glr-thumbnail-title">Setting up a custom model</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Polynomial basis functions">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_basis_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_basis.py`

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      <div class="sphx-glr-thumbnail-title">Polynomial basis functions</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Introduction ^^^^^^^^^^^^ It is possible to accelerate the identification of the gPC coefficien...">

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  .. image:: /auto_gpc/images/thumb/sphx_glr_plot_gradient_enhanced_gpc_thumb.png
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  :ref:`sphx_glr_auto_gpc_plot_gradient_enhanced_gpc.py`

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      <div class="sphx-glr-thumbnail-title">Gradient enhanced gPC</div>
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    </div>


.. toctree::
   :hidden:

   /auto_gpc/plot_problem
   /auto_gpc/plot_gpc_validation
   /auto_gpc/plot_projection
   /auto_gpc/plot_multi_element_gpc
   /auto_gpc/plot_model
   /auto_gpc/plot_basis
   /auto_gpc/plot_gradient_enhanced_gpc


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  .. container:: sphx-glr-footer sphx-glr-footer-gallery

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download all examples in Python source code: auto_gpc_python.zip </auto_gpc/auto_gpc_python.zip>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download all examples in Jupyter notebooks: auto_gpc_jupyter.zip </auto_gpc/auto_gpc_jupyter.zip>`


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 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_