Note
Go to the end to download the full example code.
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_surrogate
from gemseo import sample_disciplines
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 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
)
WARNING - 15:34:57: No coupling in MDA, switching chain_linearize to True.
INFO - 15:34:57: *** Start Sampling execution ***
INFO - 15:34:57: Sampling
INFO - 15:34:57: Disciplines: func
INFO - 15:34:57: MDO formulation: MDF
INFO - 15:34:57: Running the algorithm PYDOE_FULLFACT:
INFO - 15:34:57: 11%|█ | 1/9 [00:00<00:00, 380.16 it/sec]
INFO - 15:34:57: 22%|██▏ | 2/9 [00:00<00:00, 637.19 it/sec]
INFO - 15:34:57: 33%|███▎ | 3/9 [00:00<00:00, 825.92 it/sec]
INFO - 15:34:57: 44%|████▍ | 4/9 [00:00<00:00, 986.43 it/sec]
INFO - 15:34:57: 56%|█████▌ | 5/9 [00:00<00:00, 1112.67 it/sec]
INFO - 15:34:57: 67%|██████▋ | 6/9 [00:00<00:00, 1226.34 it/sec]
INFO - 15:34:57: 78%|███████▊ | 7/9 [00:00<00:00, 1312.54 it/sec]
INFO - 15:34:57: 89%|████████▉ | 8/9 [00:00<00:00, 1392.30 it/sec]
INFO - 15:34:57: 100%|██████████| 9/9 [00:00<00:00, 1468.48 it/sec]
INFO - 15:34:57: *** End Sampling execution (time: 0:00:00.007452) ***
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])})
{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([6.03823018]), 'y_2': array([-6.03823018])}
Total running time of the script: (0 minutes 0.099 seconds)