.. 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 ` 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 .. 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", 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 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 70-75 .. 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 - 00:11:48: INFO - 00:11:48: *** Start DOEScenario execution *** INFO - 00:11:48: DOEScenario INFO - 00:11:48: Disciplines: func INFO - 00:11:48: MDO formulation: DisciplinaryOpt INFO - 00:11:48: Optimization problem: INFO - 00:11:48: minimize y_1(x_1, x_2) INFO - 00:11:48: with respect to x_1, x_2 INFO - 00:11:48: over the design space: INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: | Name | Lower bound | Value | Upper bound | Type | INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: | x_1 | 0 | None | 1 | float | INFO - 00:11:48: | x_2 | 0 | None | 1 | float | INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: Solving optimization problem with algorithm fullfact: INFO - 00:11:48: 11%|█ | 1/9 [00:00<00:00, 382.41 it/sec, obj=1] INFO - 00:11:48: 22%|██▏ | 2/9 [00:00<00:00, 606.90 it/sec, obj=2] INFO - 00:11:48: 33%|███▎ | 3/9 [00:00<00:00, 775.77 it/sec, obj=3] INFO - 00:11:48: 44%|████▍ | 4/9 [00:00<00:00, 904.38 it/sec, obj=2.5] INFO - 00:11:48: 56%|█████▌ | 5/9 [00:00<00:00, 1004.05 it/sec, obj=3.5] INFO - 00:11:48: 67%|██████▋ | 6/9 [00:00<00:00, 1084.55 it/sec, obj=4.5] INFO - 00:11:48: 78%|███████▊ | 7/9 [00:00<00:00, 1131.41 it/sec, obj=4] INFO - 00:11:48: 89%|████████▉ | 8/9 [00:00<00:00, 1178.67 it/sec, obj=5] INFO - 00:11:48: 100%|██████████| 9/9 [00:00<00:00, 1215.35 it/sec, obj=6] INFO - 00:11:48: Optimization result: INFO - 00:11:48: Optimizer info: INFO - 00:11:48: Status: None INFO - 00:11:48: Message: None INFO - 00:11:48: Number of calls to the objective function by the optimizer: 9 INFO - 00:11:48: Solution: INFO - 00:11:48: Objective: 1.0 INFO - 00:11:48: Design space: INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: | Name | Lower bound | Value | Upper bound | Type | INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: | x_1 | 0 | 0 | 1 | float | INFO - 00:11:48: | x_2 | 0 | 0 | 1 | float | INFO - 00:11:48: +------+-------------+-------+-------------+-------+ INFO - 00:11:48: *** End DOEScenario execution (time: 0:00:00.018793) *** {'eval_jac': False, 'n_samples': 9, 'algo': 'fullfact'} .. GENERATED FROM PYTHON SOURCE LINES 76-80 Create the regression model --------------------------- Then, we build the linear regression model from the database and displays this model. .. GENERATED FROM PYTHON SOURCE LINES 80-85 .. code-block:: Python dataset = scenario.to_dataset(opt_naming=False) model = create_regression_model("GaussianProcessRegressor", data=dataset) model.learn() model .. raw:: html
GaussianProcessRegressor(alpha=1e-10, kernel=Matern, n_restarts_optimizer=10, optimizer=fmin_l_bfgs_b, random_state=0)
  • based on the scikit-learn library
  • built from 9 learning samples


.. GENERATED FROM PYTHON SOURCE LINES 86-89 Predict output -------------- Once it is built, we can use it for prediction. .. GENERATED FROM PYTHON SOURCE LINES 89-92 .. 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([8.50166028])} .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.116 seconds) .. _sphx_glr_download_examples_mlearning_regression_model_plot_gp_regression.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_gp_regression.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_gp_regression.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_