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.. 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

        Click :ref:`here <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 a :class:`.MLRegressionAlgo`

.. GENERATED FROM PYTHON SOURCE LINES 35-42

.. code-block:: default

    from gemseo.api import configure_logger
    from gemseo.api import create_design_space
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.api import create_surrogate
    from numpy import array








.. GENERATED FROM PYTHON SOURCE LINES 43-45

Import
------

.. GENERATED FROM PYTHON SOURCE LINES 45-49

.. code-block:: default


    configure_logger()






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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 50-54

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

.. GENERATED FROM PYTHON SOURCE LINES 54-59

.. code-block:: default

    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:: default

    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)








.. GENERATED FROM PYTHON SOURCE LINES 68-73

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 73-78

.. code-block:: default

    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

 Out:

 .. code-block:: none

        INFO - 07:17:18:  
        INFO - 07:17:18: *** Start DOEScenario execution ***
        INFO - 07:17:18: DOEScenario
        INFO - 07:17:18:    Disciplines: func
        INFO - 07:17:18:    MDO formulation: DisciplinaryOpt
        INFO - 07:17:18: Optimization problem:
        INFO - 07:17:18:    minimize y_1(x_1, x_2)
        INFO - 07:17:18:    with respect to x_1, x_2
        INFO - 07:17:18:    over the design space:
        INFO - 07:17:18:    +------+-------------+-------+-------------+-------+
        INFO - 07:17:18:    | name | lower_bound | value | upper_bound | type  |
        INFO - 07:17:18:    +------+-------------+-------+-------------+-------+
        INFO - 07:17:18:    | x_1  |      0      |  None |      1      | float |
        INFO - 07:17:18:    | x_2  |      0      |  None |      1      | float |
        INFO - 07:17:18:    +------+-------------+-------+-------------+-------+
        INFO - 07:17:18: Solving optimization problem with algorithm fullfact:
        INFO - 07:17:18: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 9 samples: 3
        INFO - 07:17:18: Final number of samples for DOE = 9 vs 9 requested
        INFO - 07:17:18: ...   0%|          | 0/9 [00:00<?, ?it]
        INFO - 07:17:18: ... 100%|██████████| 9/9 [00:00<00:00, 1367.21 it/sec, obj=6]
        INFO - 07:17:18: Optimization result:
        INFO - 07:17:18:    Optimizer info:
        INFO - 07:17:18:       Status: None
        INFO - 07:17:18:       Message: None
        INFO - 07:17:18:       Number of calls to the objective function by the optimizer: 9
        INFO - 07:17:18:    Solution:
        INFO - 07:17:18:       Objective: 1.0
        INFO - 07:17:18:       Design space:
        INFO - 07:17:18:       +------+-------------+-------+-------------+-------+
        INFO - 07:17:18:       | name | lower_bound | value | upper_bound | type  |
        INFO - 07:17:18:       +------+-------------+-------+-------------+-------+
        INFO - 07:17:18:       | x_1  |      0      |   0   |      1      | float |
        INFO - 07:17:18:       | x_2  |      0      |   0   |      1      | float |
        INFO - 07:17:18:       +------+-------------+-------+-------------+-------+
        INFO - 07:17:18: *** End DOEScenario execution (time: 0:00:00.015389) ***

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



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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:: default

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





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

 Out:

 .. code-block:: none

        INFO - 07:17:18: Build the surrogate discipline: GPR_DOEScenario
        INFO - 07:17:18:    Dataset name: DOEScenario
        INFO - 07:17:18:    Dataset size: 9
        INFO - 07:17:18:    Surrogate model: GaussianProcessRegressor
        INFO - 07:17:18: Use the surrogate discipline: GPR_DOEScenario
        INFO - 07:17:18:    Inputs: x_1, x_2
        INFO - 07:17:18:    Outputs: y_1
        INFO - 07:17:18:    Jacobian: use finite differences




.. GENERATED FROM PYTHON SOURCE LINES 87-91

Predict output
--------------
Once it is built, we can use it for prediction, either with default inputs
or with user-defined ones.

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.. code-block:: default

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




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

 Out:

 .. code-block:: none

    {'x_1': array([0.5]), 'x_2': array([0.5]), 'y_1': array([3.49999999])}
    {'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([8.50166027])}





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

   **Total running time of the script:** ( 0 minutes  0.153 seconds)


.. _sphx_glr_download_examples_surrogate_plot_surrogate_discipline.py:


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 .. container:: sphx-glr-footer
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     :download:`Download Python source code: plot_surrogate_discipline.py <plot_surrogate_discipline.py>`



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