Error from surrogate discipline

from numpy import array
from numpy import newaxis
from numpy import sin

from gemseo.datasets.io_dataset import IODataset
from gemseo.disciplines.surrogate import SurrogateDiscipline

The quality of a SurrogateDiscipline can easily be quantified from its methods get_error_measure().

To illustrate this point, let us consider the function \(f(x)=(6x-2)^2\sin(12x-4)\) [FSK08]:

def f(x):
    return (6 * x - 2) ** 2 * sin(12 * x - 4)

and try to approximate it with an RBFRegressor.

For this, we can take these 7 learning input points

x_train = array([0.1, 0.3, 0.5, 0.6, 0.8, 0.9, 0.95])

and evaluate the model f over this design of experiments (DOE):

y_train = f(x_train)

Then, we create an IODataset from these 7 learning samples:

dataset_train = IODataset()
dataset_train.add_input_group(x_train[:, newaxis], ["x"])
dataset_train.add_output_group(y_train[:, newaxis], ["y"])

and build a SurrogateDiscipline from it:

surrogate_discipline = SurrogateDiscipline("RBFRegressor", dataset_train)

Lastly, we can get its R2Measure

r2 = surrogate_discipline.get_error_measure("R2Measure")

and evaluate it:

r2.compute_learning_measure()

array([1.])

In presence of additional data, the generalization quality can also be approximated:

x_test = array([0.2, 0.4, 0.7])
y_test = f(x_test)
dataset_test = IODataset()
dataset_test.add_input_group(x_test[:, newaxis], ["x"])
dataset_test.add_output_group(y_test[:, newaxis], ["y"])
result = r2.compute_test_measure(dataset_test)
r2.compute_test_measure(dataset_test)

array([0.98752693])

We can conclude that the regression model on which the SurrogateDiscipline is based is a very good approximation of the original function \(f\).