Create a surrogate discipline

We want to build an Discipline 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 an BaseRegressor.

from __future__ import annotations

from numpy import array

from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_surrogate
from gemseo import sample_disciplines

Create the discipline to learn

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

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
)

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

Create the training dataset

We can build a training dataset by sampling the discipline using the sample_disciplines() with a full factorial design of experiments.

dataset = sample_disciplines(
    [discipline], design_space, ["y_1", "y_2"], algo_name="PYDOE_FULLFACT", n_samples=9
)

INFO - 16:24:18: *** Start Sampling execution ***
INFO - 16:24:18: Sampling
INFO - 16:24:18:    Disciplines: func
INFO - 16:24:18:    MDO formulation: MDF
INFO - 16:24:18: Running the algorithm PYDOE_FULLFACT:
INFO - 16:24:18:     11%|█         | 1/9 [00:00<00:00, 420.27 it/sec]
INFO - 16:24:18:     22%|██▏       | 2/9 [00:00<00:00, 714.35 it/sec]
INFO - 16:24:18:     33%|███▎      | 3/9 [00:00<00:00, 950.59 it/sec]
INFO - 16:24:18:     44%|████▍     | 4/9 [00:00<00:00, 1148.89 it/sec]
INFO - 16:24:18:     56%|█████▌    | 5/9 [00:00<00:00, 1316.23 it/sec]
INFO - 16:24:18:     67%|██████▋   | 6/9 [00:00<00:00, 1450.90 it/sec]
INFO - 16:24:18:     78%|███████▊  | 7/9 [00:00<00:00, 1576.04 it/sec]
INFO - 16:24:18:     89%|████████▉ | 8/9 [00:00<00:00, 1685.47 it/sec]
INFO - 16:24:18:    100%|██████████| 9/9 [00:00<00:00, 1751.44 it/sec]
INFO - 16:24:18: *** End Sampling execution ***

Create the surrogate discipline

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

model = create_surrogate("GaussianProcessRegressor", data=dataset)

Predict output

Once it is built, we can use it for prediction, either with default inputs

model.execute()

{'x_1': array([0.5]), 'x_2': array([0.5]), 'y_1': array([3.5]), 'y_2': array([-3.5])}

or with user-defined ones.

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

 WARNING - 16:24:18: The surrogate discipline GPR_Sampling is used at an input point outside its domain of validity: {'x_1': array([1.]), 'x_2': array([2.])}.

{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([6.03823007]), 'y_2': array([-6.03823007])}