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 __future__ import division, unicode_literals
Import¶
from numpy import array
from gemseo.api import (
configure_logger,
create_design_space,
create_discipline,
create_scenario,
create_surrogate,
)
configure_logger()
Out:
<RootLogger root (INFO)>
Create the discipline to learn¶
We can implement this analytic discipline by means of the
AnalyticDiscipline
class.
expressions_dict = {"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_dict=expressions_dict
)
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.
discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)
scenario = create_scenario(
[discipline], "DisciplinaryOpt", "y_1", design_space, scenario_type="DOE"
)
scenario.execute({"algo": "fullfact", "n_samples": 9})
Out:
INFO - 12:57:07:
INFO - 12:57:07: *** Start DOE Scenario execution ***
INFO - 12:57:07: DOEScenario
INFO - 12:57:07: Disciplines: func
INFO - 12:57:07: MDOFormulation: DisciplinaryOpt
INFO - 12:57:07: Algorithm: fullfact
INFO - 12:57:07: Optimization problem:
INFO - 12:57:07: Minimize: y_1(x_1, x_2)
INFO - 12:57:07: With respect to: x_1, x_2
INFO - 12:57:07: Full factorial design required. Number of samples along each direction for a design vector of size 2 with 9 samples: 3
INFO - 12:57:07: Final number of samples for DOE = 9 vs 9 requested
INFO - 12:57:07: DOE sampling: 0%| | 0/9 [00:00<?, ?it]
INFO - 12:57:07: DOE sampling: 100%|██████████| 9/9 [00:00<00:00, 586.50 it/sec, obj=6]
INFO - 12:57:07: Optimization result:
INFO - 12:57:07: Objective value = 1.0
INFO - 12:57:07: The result is feasible.
INFO - 12:57:07: Status: None
INFO - 12:57:07: Optimizer message: None
INFO - 12:57:07: Number of calls to the objective function by the optimizer: 9
INFO - 12:57:07: Design space:
INFO - 12:57:07: +------+-------------+-------+-------------+-------+
INFO - 12:57:07: | name | lower_bound | value | upper_bound | type |
INFO - 12:57:07: +------+-------------+-------+-------------+-------+
INFO - 12:57:07: | x_1 | 0 | 0 | 1 | float |
INFO - 12:57:07: | x_2 | 0 | 0 | 1 | float |
INFO - 12:57:07: +------+-------------+-------+-------------+-------+
INFO - 12:57:07: *** DOE Scenario run terminated ***
{'eval_jac': False, 'algo': 'fullfact', 'n_samples': 9}
Create the surrogate discipline¶
Then, we build the Gaussian process regression model from the discipline cache and displays this model.
dataset = discipline.cache.export_to_dataset()
model = create_surrogate("GaussianProcessRegression", data=dataset)
Out:
INFO - 12:57:07: Build the surrogate discipline: GPR_func
INFO - 12:57:07: Dataset name: func
INFO - 12:57:07: Dataset size: 9
INFO - 12:57:07: Surrogate model: GaussianProcessRegression
INFO - 12:57:07: Use the surrogate discipline: GPR_func
INFO - 12:57:07: Inputs: x_1, x_2
INFO - 12:57:07: Outputs: y_1, y_2
INFO - 12:57:07: 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]), 'y_2': array([-3.50000001])}
{'x_1': array([1.]), 'x_2': array([2.]), 'y_1': array([8.50166027]), 'y_2': array([-8.56035161])}
Total running time of the script: ( 0 minutes 0.151 seconds)