Create a surrogate discipline

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

  • \(y_1=1+2x_1+3x_2\)

  • \(y_2=-1-2x_1-3x_2\)

over the unit hypercube \([0,1]\times[0,1]\). For that, we use a SurrogateDiscipline relying on a MLRegressionAlgo

from __future__ import absolute_import, division, print_function, unicode_literals

from future import standard_library

Import

from numpy import array

from gemseo.api import (
    configure_logger,
    create_design_space,
    create_discipline,
    create_scenario,
    create_surrogate,
)

configure_logger()


standard_library.install_aliases()

Create the discipline to learn

We can implement this analytic discipline by means of the AnalyticDiscipline class.

expressions_dict = {"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_dict=expressions_dict
)

Create the input sampling space

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

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)

Create the learning set

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

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

Out:

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

Create the surrogate discipline

Then, we build the Gaussian process regression model from the discipline cache and displays this model.

dataset = discipline.cache.export_to_dataset()
model = create_surrogate("GaussianProcessRegression", data=dataset)

Predict output

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

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

Out:

{'x_1': array([0.]), 'x_2': array([0.]), 'y_1': array([1.]), 'y_2': array([-1.])}
{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([3.91371997]), 'y_2': array([-3.91371997])}

Total running time of the script: ( 0 minutes 0.182 seconds)

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