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 configure_logger
from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import create_surrogate

Import

configure_logger()

<RootLogger root (INFO)>

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 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.

scenario = create_scenario(
    [discipline],
    "y_1",
    design_space,
    scenario_type="DOE",
    formulation_name="DisciplinaryOpt",
)
scenario.execute(algo_name="PYDOE_FULLFACT", n_samples=9)

INFO - 08:37:19:
INFO - 08:37:19: *** Start DOEScenario execution ***
INFO - 08:37:19: DOEScenario
INFO - 08:37:19:    Disciplines: func
INFO - 08:37:19:    MDO formulation: DisciplinaryOpt
INFO - 08:37:19: Optimization problem:
INFO - 08:37:19:    minimize y_1(x_1, x_2)
INFO - 08:37:19:    with respect to x_1, x_2
INFO - 08:37:19:    over the design space:
INFO - 08:37:19:       +------+-------------+-------+-------------+-------+
INFO - 08:37:19:       | Name | Lower bound | Value | Upper bound | Type  |
INFO - 08:37:19:       +------+-------------+-------+-------------+-------+
INFO - 08:37:19:       | x_1  |      0      |  None |      1      | float |
INFO - 08:37:19:       | x_2  |      0      |  None |      1      | float |
INFO - 08:37:19:       +------+-------------+-------+-------------+-------+
INFO - 08:37:19: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 08:37:19:     11%|█         | 1/9 [00:00<00:00, 392.03 it/sec, obj=1]
INFO - 08:37:19:     22%|██▏       | 2/9 [00:00<00:00, 652.20 it/sec, obj=2]
INFO - 08:37:19:     33%|███▎      | 3/9 [00:00<00:00, 857.09 it/sec, obj=3]
INFO - 08:37:19:     44%|████▍     | 4/9 [00:00<00:00, 1019.71 it/sec, obj=2.5]
INFO - 08:37:19:     56%|█████▌    | 5/9 [00:00<00:00, 1144.30 it/sec, obj=3.5]
INFO - 08:37:19:     67%|██████▋   | 6/9 [00:00<00:00, 1249.36 it/sec, obj=4.5]
INFO - 08:37:19:     78%|███████▊  | 7/9 [00:00<00:00, 1337.96 it/sec, obj=4]
INFO - 08:37:19:     89%|████████▉ | 8/9 [00:00<00:00, 1415.68 it/sec, obj=5]
INFO - 08:37:19:    100%|██████████| 9/9 [00:00<00:00, 1483.60 it/sec, obj=6]
INFO - 08:37:19: Optimization result:
INFO - 08:37:19:    Optimizer info:
INFO - 08:37:19:       Status: None
INFO - 08:37:19:       Message: None
INFO - 08:37:19:       Number of calls to the objective function by the optimizer: 9
INFO - 08:37:19:    Solution:
INFO - 08:37:19:       Objective: 1.0
INFO - 08:37:19:       Design space:
INFO - 08:37:19:          +------+-------------+-------+-------------+-------+
INFO - 08:37:19:          | Name | Lower bound | Value | Upper bound | Type  |
INFO - 08:37:19:          +------+-------------+-------+-------------+-------+
INFO - 08:37:19:          | x_1  |      0      |   0   |      1      | float |
INFO - 08:37:19:          | x_2  |      0      |   0   |      1      | float |
INFO - 08:37:19:          +------+-------------+-------+-------------+-------+
INFO - 08:37:19: *** End DOEScenario execution (time: 0:00:00.010125) ***

Create the surrogate discipline

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

dataset = scenario.to_dataset(opt_naming=False)
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])}

or with user-defined ones.

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

{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([6.03823023])}