Note
Click here to download the full example code
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)