.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/mlearning/regression_model/plot_pce_regression.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_mlearning_regression_model_plot_pce_regression.py: PCE 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 32-44 .. 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_parameter_space from gemseo.api import create_scenario from gemseo.mlearning.api import create_regression_model from gemseo.mlearning.api import import_regression_model from numpy import array configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 45-49 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 49-54 .. 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 ) .. GENERATED FROM PYTHON SOURCE LINES 55-58 Create the input sampling space ------------------------------- We create the input sampling space by adding the variables one by one. .. GENERATED FROM PYTHON SOURCE LINES 58-62 .. 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 63-68 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 68-73 .. 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 - 10:08:48: INFO - 10:08:48: *** Start DOEScenario execution *** INFO - 10:08:48: DOEScenario INFO - 10:08:48: Disciplines: func INFO - 10:08:48: MDO formulation: DisciplinaryOpt INFO - 10:08:48: Optimization problem: INFO - 10:08:48: minimize y_1(x_1, x_2) INFO - 10:08:48: with respect to x_1, x_2 INFO - 10:08:48: over the design space: INFO - 10:08:48: +------+-------------+-------+-------------+-------+ INFO - 10:08:48: | name | lower_bound | value | upper_bound | type | INFO - 10:08:48: +------+-------------+-------+-------------+-------+ INFO - 10:08:48: | x_1 | 0 | None | 1 | float | INFO - 10:08:48: | x_2 | 0 | None | 1 | float | INFO - 10:08:48: +------+-------------+-------+-------------+-------+ INFO - 10:08:48: Solving optimization problem with algorithm fullfact: INFO - 10:08:48: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 9 samples: 3 INFO - 10:08:48: Final number of samples for DOE = 9 vs 9 requested INFO - 10:08:48: ... 0%| | 0/9 [00:00, sparse_param=None, stieltjes=True, strategy='LS') based on the OpenTURNS library built from 9 learning samples .. GENERATED FROM PYTHON SOURCE LINES 89-92 Predict output -------------- Once it is built, we can use it for prediction. .. GENERATED FROM PYTHON SOURCE LINES 92-96 .. code-block:: default input_value = {"x_1": array([1.0]), "x_2": array([2.0])} output_value = model.predict(input_value) print(output_value) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none {'y_1': array([9.])} .. GENERATED FROM PYTHON SOURCE LINES 97-100 Save the regression model ------------------------- Lastly, we save the model. .. GENERATED FROM PYTHON SOURCE LINES 100-102 .. code-block:: default directory = model.save() .. GENERATED FROM PYTHON SOURCE LINES 103-106 Load the regression model ------------------------- In an other study, we could load this model. .. GENERATED FROM PYTHON SOURCE LINES 106-109 .. code-block:: default loaded_model = import_regression_model(directory) print(loaded_model) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none PCERegressor(degree=2, n_quad=None, probability_space=, sparse_param=None, stieltjes=True, strategy='LS') based on the OpenTURNS library built from 0 learning samples .. GENERATED FROM PYTHON SOURCE LINES 110-113 Use the loaded regression model ------------------------------- And use it! .. GENERATED FROM PYTHON SOURCE LINES 113-114 .. code-block:: default print(loaded_model.predict(input_value)) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none {'y_1': array([9.])} .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.169 seconds) .. _sphx_glr_download_examples_mlearning_regression_model_plot_pce_regression.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:Download Python source code: plot_pce_regression.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: plot_pce_regression.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _