.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/post_process/algorithms/plot_som.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_post_process_algorithms_plot_som.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_post_process_algorithms_plot_som.py:


Self-Organizing Map
===================

In this example, we illustrate the use of the :class:`.SOM` plot
on the Sobieski's SSBJ problem.

The :class:`.SOM` post-processing performs a Self Organizing Map clustering on the
optimization history. A :class:`.SOM` is a 2D representation of a design of experiments
which requires dimensionality reduction since it may be in a very high dimension.

A :term:`SOM` is built by using an unsupervised artificial neural network
:cite:`Kohonen:2001`. A map of size ``n_x.n_y`` is generated, where ``n_x`` is the
number of neurons in the :math:`x` direction and ``n_y`` is the number of neurons in the
:math:`y` direction. The design space (whatever the dimension) is reduced to a 2D
representation based on ``n_x.n_y`` neurons. Samples are clustered to a neuron when
their design variables are close in terms of their L2 norm. A neuron is always located
at the same place on a map. Each neuron is colored according to the average value for
a given criterion. This helps to qualitatively analyze whether parts of the design
space are good according to some criteria and not for others, and where compromises
should be made. A white neuron has no sample associated with it: not enough evaluations
were provided to train the SOM.

SOM's provide a qualitative view of the :term:`objective function`, the
:term:`constraints`, and of their relative behaviors.

.. GENERATED FROM PYTHON SOURCE LINES 47-58

.. code-block:: Python


    from __future__ import annotations

    from gemseo import execute_post
    from gemseo.settings.post import SOM_Settings

    execute_post(
        "sobieski_mdf_scenario.h5",
        settings_model=SOM_Settings(save=False, show=True),
    )




.. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_som_001.png
   :alt: Self Organizing Maps of the design space, -y_4, g_1[0], g_1[1], g_1[2], g_1[3], g_1[4], g_1[5], g_1[6], g_2, g_3[0], g_3[1], g_3[2], g_3[3]
   :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_som_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <gemseo.post.som.SOM object at 0x7f524c7808f0>



.. GENERATED FROM PYTHON SOURCE LINES 59-78

The following figure illustrates another :term:`SOM` on the Sobieski
use case. The optimization method is a (costly) derivative free algorithm
(``NLOPT_COBYLA``), indeed all the relevant information for the optimization
is obtained at the cost of numerous evaluations of the functions. For
more details, please read the paper by
:cite:`kumano2006multidisciplinary` on wing MDO post-processing
using SOM.

.. figure:: /tutorials/ssbj/figs/MDOScenario_SOM_v100.png

    SOM example on the Sobieski problem.

A DOE may also be a good way to produce SOM maps.
The following figure shows an example with 10000 points on
the same test case. This produces more relevant SOM plots.

.. figure:: /tutorials/ssbj/figs/som_fine.png

    SOM example on the Sobieski problem with a 10 000 samples DOE.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.888 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_som.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: plot_som.ipynb <plot_som.ipynb>`

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

      :download:`Download Python source code: plot_som.py <plot_som.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_som.zip <plot_som.zip>`


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

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