Note
Click here to download the full example code
Create a surrogate discipline¶
We want to build an 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 gemseo.api import configure_logger
from gemseo.api import create_design_space
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.api import create_surrogate
from numpy import array
Import¶
configure_logger()
Out:
<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", 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.
scenario = create_scenario(
[discipline], "DisciplinaryOpt", "y_1", design_space, scenario_type="DOE"
)
scenario.execute({"algo": "fullfact", "n_samples": 9})
Out:
INFO - 07:17:18:
INFO - 07:17:18: *** Start DOEScenario execution ***
INFO - 07:17:18: DOEScenario
INFO - 07:17:18: Disciplines: func
INFO - 07:17:18: MDO formulation: DisciplinaryOpt
INFO - 07:17:18: Optimization problem:
INFO - 07:17:18: minimize y_1(x_1, x_2)
INFO - 07:17:18: with respect to x_1, x_2
INFO - 07:17:18: over the design space:
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: | name | lower_bound | value | upper_bound | type |
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: | x_1 | 0 | None | 1 | float |
INFO - 07:17:18: | x_2 | 0 | None | 1 | float |
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: Solving optimization problem with algorithm fullfact:
INFO - 07:17:18: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 9 samples: 3
INFO - 07:17:18: Final number of samples for DOE = 9 vs 9 requested
INFO - 07:17:18: ... 0%| | 0/9 [00:00<?, ?it]
INFO - 07:17:18: ... 100%|██████████| 9/9 [00:00<00:00, 1367.21 it/sec, obj=6]
INFO - 07:17:18: Optimization result:
INFO - 07:17:18: Optimizer info:
INFO - 07:17:18: Status: None
INFO - 07:17:18: Message: None
INFO - 07:17:18: Number of calls to the objective function by the optimizer: 9
INFO - 07:17:18: Solution:
INFO - 07:17:18: Objective: 1.0
INFO - 07:17:18: Design space:
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: | name | lower_bound | value | upper_bound | type |
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: | x_1 | 0 | 0 | 1 | float |
INFO - 07:17:18: | x_2 | 0 | 0 | 1 | float |
INFO - 07:17:18: +------+-------------+-------+-------------+-------+
INFO - 07:17:18: *** End DOEScenario execution (time: 0:00:00.015389) ***
{'eval_jac': False, 'algo': 'fullfact', 'n_samples': 9}
Create the surrogate discipline¶
Then, we build the Gaussian process regression model from the database and displays this model.
dataset = scenario.export_to_dataset(opt_naming=False)
model = create_surrogate("GaussianProcessRegressor", data=dataset)
Out:
INFO - 07:17:18: Build the surrogate discipline: GPR_DOEScenario
INFO - 07:17:18: Dataset name: DOEScenario
INFO - 07:17:18: Dataset size: 9
INFO - 07:17:18: Surrogate model: GaussianProcessRegressor
INFO - 07:17:18: Use the surrogate discipline: GPR_DOEScenario
INFO - 07:17:18: Inputs: x_1, x_2
INFO - 07:17:18: Outputs: y_1
INFO - 07:17:18: Jacobian: use finite differences
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([0.5]), 'x_2': array([0.5]), 'y_1': array([3.49999999])}
{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([8.50166027])}
Total running time of the script: ( 0 minutes 0.153 seconds)