Note
Go to the end to download the full example code.
GP regression#
We want to approximate a 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 \([0,1]\times[0,1]\).
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()
<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 - 13:27:07:
INFO - 13:27:07: *** Start DOEScenario execution ***
INFO - 13:27:07: DOEScenario
INFO - 13:27:07: Disciplines: func
INFO - 13:27:07: MDO formulation: DisciplinaryOpt
INFO - 13:27:07: Optimization problem:
INFO - 13:27:07: minimize y_1(x_1, x_2)
INFO - 13:27:07: with respect to x_1, x_2
INFO - 13:27:07: over the design space:
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: | x_1 | 0 | None | 1 | float |
INFO - 13:27:07: | x_2 | 0 | None | 1 | float |
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: Solving optimization problem with algorithm PYDOE_FULLFACT:
INFO - 13:27:07: 11%|█ | 1/9 [00:00<00:00, 361.77 it/sec, obj=1]
INFO - 13:27:07: 22%|██▏ | 2/9 [00:00<00:00, 612.58 it/sec, obj=2]
INFO - 13:27:07: 33%|███▎ | 3/9 [00:00<00:00, 810.18 it/sec, obj=3]
INFO - 13:27:07: 44%|████▍ | 4/9 [00:00<00:00, 971.18 it/sec, obj=2.5]
INFO - 13:27:07: 56%|█████▌ | 5/9 [00:00<00:00, 1103.42 it/sec, obj=3.5]
INFO - 13:27:07: 67%|██████▋ | 6/9 [00:00<00:00, 1214.16 it/sec, obj=4.5]
INFO - 13:27:07: 78%|███████▊ | 7/9 [00:00<00:00, 1305.18 it/sec, obj=4]
INFO - 13:27:07: 89%|████████▉ | 8/9 [00:00<00:00, 1384.54 it/sec, obj=5]
INFO - 13:27:07: 100%|██████████| 9/9 [00:00<00:00, 1447.53 it/sec, obj=6]
INFO - 13:27:07: Optimization result:
INFO - 13:27:07: Optimizer info:
INFO - 13:27:07: Status: None
INFO - 13:27:07: Message: None
INFO - 13:27:07: Number of calls to the objective function by the optimizer: 9
INFO - 13:27:07: Solution:
INFO - 13:27:07: Objective: 1.0
INFO - 13:27:07: Design space:
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: | Name | Lower bound | Value | Upper bound | Type |
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: | x_1 | 0 | 0 | 1 | float |
INFO - 13:27:07: | x_2 | 0 | 0 | 1 | float |
INFO - 13:27:07: +------+-------------+-------+-------------+-------+
INFO - 13:27:07: *** End DOEScenario execution (time: 0:00:00.010377) ***
Create the regression model#
Then, we build the linear regression model from the database and displays this model.
dataset = scenario.to_dataset(opt_naming=False)
model = create_regression_model("GaussianProcessRegressor", data=dataset)
model.learn()
model
Predict output#
Once it is built, we can use it for prediction.
input_value = {"x_1": array([1.0]), "x_2": array([2.0])}
output_value = model.predict(input_value)
output_value
{'y_1': array([6.03823023])}
Total running time of the script: (0 minutes 0.095 seconds)