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

.. only:: html

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

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

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

.. _sphx_glr_examples_surrogate_plot_surrogate_discipline.py:


Create a surrogate discipline
=============================

We want to build an :class:`.MDODiscipline`
based on a regression model approximating the following discipline
with two inputs and two outputs:

- :math:`y_1=1+2x_1+3x_2`
- :math:`y_2=-1-2x_1-3x_2`

over the unit hypercube :math:`[0,1]\times[0,1]`.
For that, we use a :class:`.SurrogateDiscipline` relying on an :class:`.MLRegressionAlgo`

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.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo import configure_logger
    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import create_surrogate








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Import
------

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.. code-block:: Python


    configure_logger()






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 .. code-block:: none


    <RootLogger root (INFO)>



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Create the discipline to learn
------------------------------
We can implement this analytic discipline by means of the
:class:`~gemseo.disciplines.analytic.AnalyticDiscipline` class.

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.. code-block:: Python

    expressions = {"y_1": "1+2*x_1+3*x_2", "y_2": "-1-2*x_1-3*x_2"}
    discipline = create_discipline(
        "AnalyticDiscipline", name="func", expressions=expressions
    )








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Create the input sampling space
-------------------------------
We create the input sampling space by adding the variables one by one.

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.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x_1", l_b=0.0, u_b=1.0)
    design_space.add_variable("x_2", l_b=0.0, u_b=1.0)








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Create the learning set
-----------------------
We can build a learning set by means of a
:class:`~gemseo.core.doe_scenario.DOEScenario` with a full factorial design of
experiments. The number of samples can be equal to 9 for example.

.. GENERATED FROM PYTHON SOURCE LINES 77-82

.. code-block:: Python

    scenario = create_scenario(
        [discipline], "DisciplinaryOpt", "y_1", design_space, scenario_type="DOE"
    )
    scenario.execute({"algo": "fullfact", "n_samples": 9})





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

 .. code-block:: none

        INFO - 13:54:59:  
        INFO - 13:54:59: *** Start DOEScenario execution ***
        INFO - 13:54:59: DOEScenario
        INFO - 13:54:59:    Disciplines: func
        INFO - 13:54:59:    MDO formulation: DisciplinaryOpt
        INFO - 13:54:59: Optimization problem:
        INFO - 13:54:59:    minimize y_1(x_1, x_2)
        INFO - 13:54:59:    with respect to x_1, x_2
        INFO - 13:54:59:    over the design space:
        INFO - 13:54:59:       +------+-------------+-------+-------------+-------+
        INFO - 13:54:59:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:54:59:       +------+-------------+-------+-------------+-------+
        INFO - 13:54:59:       | x_1  |      0      |  None |      1      | float |
        INFO - 13:54:59:       | x_2  |      0      |  None |      1      | float |
        INFO - 13:54:59:       +------+-------------+-------+-------------+-------+
        INFO - 13:54:59: Solving optimization problem with algorithm fullfact:
        INFO - 13:54:59:     11%|█         | 1/9 [00:00<00:00, 366.80 it/sec, obj=1]
        INFO - 13:54:59:     22%|██▏       | 2/9 [00:00<00:00, 579.84 it/sec, obj=2]
        INFO - 13:54:59:     33%|███▎      | 3/9 [00:00<00:00, 734.34 it/sec, obj=3]
        INFO - 13:54:59:     44%|████▍     | 4/9 [00:00<00:00, 849.91 it/sec, obj=2.5]
        INFO - 13:54:59:     56%|█████▌    | 5/9 [00:00<00:00, 938.83 it/sec, obj=3.5]
        INFO - 13:54:59:     67%|██████▋   | 6/9 [00:00<00:00, 1001.11 it/sec, obj=4.5]
        INFO - 13:54:59:     78%|███████▊  | 7/9 [00:00<00:00, 1063.62 it/sec, obj=4]
        INFO - 13:54:59:     89%|████████▉ | 8/9 [00:00<00:00, 1107.08 it/sec, obj=5]
        INFO - 13:54:59:    100%|██████████| 9/9 [00:00<00:00, 1124.71 it/sec, obj=6]
        INFO - 13:54:59: Optimization result:
        INFO - 13:54:59:    Optimizer info:
        INFO - 13:54:59:       Status: None
        INFO - 13:54:59:       Message: None
        INFO - 13:54:59:       Number of calls to the objective function by the optimizer: 9
        INFO - 13:54:59:    Solution:
        INFO - 13:54:59:       Objective: 1.0
        INFO - 13:54:59:       Design space:
        INFO - 13:54:59:          +------+-------------+-------+-------------+-------+
        INFO - 13:54:59:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 13:54:59:          +------+-------------+-------+-------------+-------+
        INFO - 13:54:59:          | x_1  |      0      |   0   |      1      | float |
        INFO - 13:54:59:          | x_2  |      0      |   0   |      1      | float |
        INFO - 13:54:59:          +------+-------------+-------+-------------+-------+
        INFO - 13:54:59: *** End DOEScenario execution (time: 0:00:00.019631) ***

    {'eval_jac': False, 'n_samples': 9, 'algo': 'fullfact'}



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Create the surrogate discipline
-------------------------------
Then, we build the Gaussian process regression model from the database and
displays this model.

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.. code-block:: Python

    dataset = scenario.to_dataset(opt_naming=False)
    model = create_surrogate("GaussianProcessRegressor", data=dataset)





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 .. code-block:: none

        INFO - 13:54:59: Build the surrogate discipline: GPR_DOEScenario
        INFO - 13:54:59:    Dataset size: 9
        INFO - 13:54:59:    Surrogate model: GaussianProcessRegressor
        INFO - 13:54:59: Use the surrogate discipline: GPR_DOEScenario
        INFO - 13:54:59:    Inputs: x_1, x_2
        INFO - 13:54:59:    Outputs: y_1
        INFO - 13:54:59:    Jacobian: use finite differences




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Predict output
--------------
Once it is built, we can use it for prediction, either with default inputs

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.. code-block:: Python

    model.execute()




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 .. code-block:: none


    {'x_2': array([0.5]), 'x_1': array([0.5]), 'y_1': array([3.49999999])}



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or with user-defined ones.

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.. code-block:: Python

    model.execute({"x_1": array([1.0]), "x_2": array([2.0])})




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

 .. code-block:: none


    {'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([8.50166028])}




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

   **Total running time of the script:** (0 minutes 0.150 seconds)


.. _sphx_glr_download_examples_surrogate_plot_surrogate_discipline.py:

.. only:: html

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

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

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

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

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


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