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

.. only:: html

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

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

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

.. _sphx_glr_examples_mlearning_regression_model_plot_gp_regression.py:


GP regression
=============

We want to approximate a 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]`.

.. GENERATED FROM PYTHON SOURCE LINES 32-46

.. 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.mlearning import create_regression_model

    configure_logger()






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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 47-51

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

.. GENERATED FROM PYTHON SOURCE LINES 51-56

.. 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
    )








.. GENERATED FROM PYTHON SOURCE LINES 57-60

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

.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x_1", lower_bound=0.0, upper_bound=1.0)
    design_space.add_variable("x_2", lower_bound=0.0, upper_bound=1.0)








.. GENERATED FROM PYTHON SOURCE LINES 65-70

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

.. GENERATED FROM PYTHON SOURCE LINES 70-79

.. code-block:: Python

    scenario = create_scenario(
        [discipline],
        "y_1",
        design_space,
        scenario_type="DOE",
        formulation_name="DisciplinaryOpt",
    )
    scenario.execute(algo_name="PYDOE_FULLFACT", n_samples=9)





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

 .. code-block:: none

        INFO - 16:13:51:  
        INFO - 16:13:51: *** Start DOEScenario execution ***
        INFO - 16:13:51: DOEScenario
        INFO - 16:13:51:    Disciplines: func
        INFO - 16:13:51:    MDO formulation: DisciplinaryOpt
        INFO - 16:13:51: Optimization problem:
        INFO - 16:13:51:    minimize y_1(x_1, x_2)
        INFO - 16:13:51:    with respect to x_1, x_2
        INFO - 16:13:51:    over the design space:
        INFO - 16:13:51:       +------+-------------+-------+-------------+-------+
        INFO - 16:13:51:       | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 16:13:51:       +------+-------------+-------+-------------+-------+
        INFO - 16:13:51:       | x_1  |      0      |  None |      1      | float |
        INFO - 16:13:51:       | x_2  |      0      |  None |      1      | float |
        INFO - 16:13:51:       +------+-------------+-------+-------------+-------+
        INFO - 16:13:51: Solving optimization problem with algorithm PYDOE_FULLFACT:
        INFO - 16:13:51:     11%|█         | 1/9 [00:00<00:00, 385.86 it/sec, obj=1]
        INFO - 16:13:51:     22%|██▏       | 2/9 [00:00<00:00, 651.85 it/sec, obj=2]
        INFO - 16:13:51:     33%|███▎      | 3/9 [00:00<00:00, 860.72 it/sec, obj=3]
        INFO - 16:13:51:     44%|████▍     | 4/9 [00:00<00:00, 1018.96 it/sec, obj=2.5]
        INFO - 16:13:51:     56%|█████▌    | 5/9 [00:00<00:00, 1147.36 it/sec, obj=3.5]
        INFO - 16:13:51:     67%|██████▋   | 6/9 [00:00<00:00, 1262.84 it/sec, obj=4.5]
        INFO - 16:13:51:     78%|███████▊  | 7/9 [00:00<00:00, 1361.03 it/sec, obj=4]
        INFO - 16:13:51:     89%|████████▉ | 8/9 [00:00<00:00, 1446.31 it/sec, obj=5]
        INFO - 16:13:51:    100%|██████████| 9/9 [00:00<00:00, 1520.96 it/sec, obj=6]
        INFO - 16:13:51: Optimization result:
        INFO - 16:13:51:    Optimizer info:
        INFO - 16:13:51:       Status: None
        INFO - 16:13:51:       Message: None
        INFO - 16:13:51:       Number of calls to the objective function by the optimizer: 9
        INFO - 16:13:51:    Solution:
        INFO - 16:13:51:       Objective: 1.0
        INFO - 16:13:51:       Design space:
        INFO - 16:13:51:          +------+-------------+-------+-------------+-------+
        INFO - 16:13:51:          | Name | Lower bound | Value | Upper bound | Type  |
        INFO - 16:13:51:          +------+-------------+-------+-------------+-------+
        INFO - 16:13:51:          | x_1  |      0      |   0   |      1      | float |
        INFO - 16:13:51:          | x_2  |      0      |   0   |      1      | float |
        INFO - 16:13:51:          +------+-------------+-------+-------------+-------+
        INFO - 16:13:51: *** End DOEScenario execution (time: 0:00:00.009775) ***




.. GENERATED FROM PYTHON SOURCE LINES 80-84

Create the regression model
---------------------------
Then, we build the linear regression model from the database and
displays this model.

.. GENERATED FROM PYTHON SOURCE LINES 84-89

.. code-block:: Python

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






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style='background-color: #fafae2; padding: 10px;'>GaussianProcessRegressor(alpha=1e-10, bounds=(), input_names=(), kernel=None, n_restarts_optimizer=10, optimizer=fmin_l_bfgs_b, output_names=(), parameters={}, random_state=0, transformer={&#x27;inputs&#x27;: &lt;gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object at 0x7f660dd294f0&gt;, &#x27;outputs&#x27;: &lt;gemseo.mlearning.transformers.scaler.min_max_scaler.MinMaxScaler object at 0x7f660dd29550&gt;})<br/><ul><li>based on the scikit-learn library</li><li>built from 9 learning samples</li></ul></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 90-93

Predict output
--------------
Once it is built, we can use it for prediction.

.. GENERATED FROM PYTHON SOURCE LINES 93-96

.. code-block:: Python

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




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

 .. code-block:: none


    {'y_1': array([6.03823023])}




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

   **Total running time of the script:** (0 minutes 0.101 seconds)


.. _sphx_glr_download_examples_mlearning_regression_model_plot_gp_regression.py:

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

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

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

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

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

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

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