:orphan:

Polynomial Chaos Expansion Examples
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^





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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 5D data.">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_friedman_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_friedman.py`

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      <div class="sphx-glr-thumbnail-title">Friedman function (5 random inputs, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 3D data.">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_exponential_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_exponential.py`

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      <div class="sphx-glr-thumbnail-title">Exponential function (3 random inputs, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 2D data for a num...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_helmholtz_thumb.png
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  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_helmholtz.py`

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      <div class="sphx-glr-thumbnail-title">2D Helmholtz eigenvalues (2 random inputs, vector-valued output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we approximate the well-known Ishigami function with a total-degree Polynomial...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_pce_ishigami_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_pce_ishigami.py`

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      <div class="sphx-glr-thumbnail-title">Ishigami function (3 random inputs, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 8D data.">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_pce_robot_arm_thumb.png
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  :ref:`sphx_glr_auto_examples_surrogates_pce_pce_robot_arm.py`

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      <div class="sphx-glr-thumbnail-title">Robot Arm function (8 random inputs, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model of a sinusoidal function with a sing...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_oakley_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_oakley.py`

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      <div class="sphx-glr-thumbnail-title">Oakley Function  (1 random input, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model of a sinusoidal function with a sing...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_sinusoidal_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_sinusoidal.py`

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      <div class="sphx-glr-thumbnail-title">Sinusoidal Function  (1 random input, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 2D data.">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_sphere_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_sphere.py`

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      <div class="sphx-glr-thumbnail-title">Sinusoidal Function  Sphere function (2 random inputs, scalar output)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, PCE is used to generate a surrogate model for a given set of 2D data.">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_camel_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_camel.py`

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      <div class="sphx-glr-thumbnail-title">Camel function (3 random inputs, scalar output)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we approximate the well-known Ishigami function with a total-degree Polynomial...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_pce_sparsity_lars_thumb.png
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  :ref:`sphx_glr_auto_examples_surrogates_pce_pce_sparsity_lars.py`

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      <div class="sphx-glr-thumbnail-title">Hyperbolic truncation and Least Angle Regression</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we use Physics-informed Polynomial Chaos Expansion for approximation and UQ of...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_pce_euler_UQ_thumb.png
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  :ref:`sphx_glr_auto_examples_surrogates_pce_pce_euler_UQ.py`

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      <div class="sphx-glr-thumbnail-title">Physics-Informed PCE: Uncertainty Quantification of Euler Beam</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we approximate a deterministic Wave Equation by Physics-informed Polynomial Ch...">

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  .. image:: /auto_examples/surrogates/pce/images/thumb/sphx_glr_plot_pce_wave_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_surrogates_pce_plot_pce_wave.py`

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      <div class="sphx-glr-thumbnail-title">Physics-Informed PCE: Deterministic Wave Equation</div>
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    </div>


.. toctree::
   :hidden:

   /auto_examples/surrogates/pce/plot_pce_friedman
   /auto_examples/surrogates/pce/plot_pce_exponential
   /auto_examples/surrogates/pce/plot_pce_helmholtz
   /auto_examples/surrogates/pce/pce_ishigami
   /auto_examples/surrogates/pce/pce_robot_arm
   /auto_examples/surrogates/pce/plot_pce_oakley
   /auto_examples/surrogates/pce/plot_pce_sinusoidal
   /auto_examples/surrogates/pce/plot_pce_sphere
   /auto_examples/surrogates/pce/plot_pce_camel
   /auto_examples/surrogates/pce/pce_sparsity_lars
   /auto_examples/surrogates/pce/pce_euler_UQ
   /auto_examples/surrogates/pce/plot_pce_wave


.. only:: html

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

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

      :download:`Download all examples in Python source code: pce_python.zip </auto_examples/surrogates/pce/pce_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: pce_jupyter.zip </auto_examples/surrogates/pce/pce_jupyter.zip>`


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

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