.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/post_process/plot_som.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_post_process_plot_som.py: Self-Organizing Map =================== In this example, we illustrate the use of the :class:`~gemseo.post.som.SOM` plot on the Sobieski's SSBJ problem. .. GENERATED FROM PYTHON SOURCE LINES 28-34 .. code-block:: default from gemseo.api import configure_logger from gemseo.api import create_discipline from gemseo.api import create_scenario from gemseo.problems.sobieski.core.problem import SobieskiProblem from matplotlib import pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 35-39 Import ------ The first step is to import some functions from the API and a method to get the design space. .. GENERATED FROM PYTHON SOURCE LINES 39-42 .. code-block:: default configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 43-67 Description ----------- The :class:`~gemseo.post.som.SOM` post-processing performs a Self Organizing Map clustering on the optimization history. A :class:`~gemseo.post.som.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 69-73 Create disciplines ------------------ At this point, we instantiate the disciplines of Sobieski's SSBJ problem: Propulsion, Aerodynamics, Structure and Mission .. GENERATED FROM PYTHON SOURCE LINES 73-82 .. code-block:: default disciplines = create_discipline( [ "SobieskiPropulsion", "SobieskiAerodynamics", "SobieskiStructure", "SobieskiMission", ] ) .. GENERATED FROM PYTHON SOURCE LINES 83-86 Create design space ------------------- We also read the design space from the :class:`.SobieskiProblem`. .. GENERATED FROM PYTHON SOURCE LINES 86-88 .. code-block:: default design_space = SobieskiProblem().design_space .. GENERATED FROM PYTHON SOURCE LINES 89-95 Create and execute scenario --------------------------- The next step is to build an MDO scenario in order to maximize the range, encoded 'y_4', with respect to the design parameters, while satisfying the inequality constraints 'g_1', 'g_2' and 'g_3'. We can use the MDF formulation, the Monte Carlo DOE algorithm and 30 samples. .. GENERATED FROM PYTHON SOURCE LINES 95-108 .. code-block:: default scenario = create_scenario( disciplines, formulation="MDF", objective_name="y_4", maximize_objective=True, design_space=design_space, scenario_type="DOE", ) scenario.set_differentiation_method("user") for constraint in ["g_1", "g_2", "g_3"]: scenario.add_constraint(constraint, "ineq") scenario.execute({"algo": "OT_MONTE_CARLO", "n_samples": 30}) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 07:15:12: INFO - 07:15:12: *** Start DOEScenario execution *** INFO - 07:15:12: DOEScenario INFO - 07:15:12: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission INFO - 07:15:12: MDO formulation: MDF INFO - 07:15:12: Optimization problem: INFO - 07:15:12: minimize -y_4(x_shared, x_1, x_2, x_3) INFO - 07:15:12: with respect to x_1, x_2, x_3, x_shared INFO - 07:15:12: subject to constraints: INFO - 07:15:12: g_1(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 07:15:12: g_2(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 07:15:12: g_3(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 07:15:12: over the design space: INFO - 07:15:12: +----------+-------------+-------+-------------+-------+ INFO - 07:15:12: | name | lower_bound | value | upper_bound | type | INFO - 07:15:12: +----------+-------------+-------+-------------+-------+ INFO - 07:15:12: | x_shared | 0.01 | 0.05 | 0.09 | float | INFO - 07:15:12: | x_shared | 30000 | 45000 | 60000 | float | INFO - 07:15:12: | x_shared | 1.4 | 1.6 | 1.8 | float | INFO - 07:15:12: | x_shared | 2.5 | 5.5 | 8.5 | float | INFO - 07:15:12: | x_shared | 40 | 55 | 70 | float | INFO - 07:15:12: | x_shared | 500 | 1000 | 1500 | float | INFO - 07:15:12: | x_1 | 0.1 | 0.25 | 0.4 | float | INFO - 07:15:12: | x_1 | 0.75 | 1 | 1.25 | float | INFO - 07:15:12: | x_2 | 0.75 | 1 | 1.25 | float | INFO - 07:15:12: | x_3 | 0.1 | 0.5 | 1 | float | INFO - 07:15:12: +----------+-------------+-------+-------------+-------+ INFO - 07:15:12: Solving optimization problem with algorithm OT_MONTE_CARLO: INFO - 07:15:12: Generation of OT_MONTE_CARLO DOE with OpenTURNS INFO - 07:15:12: ... 0%| | 0/30 [00:00` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_som.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_