Create a general linear model metamodel

In this example we create a global approximation of a model response using a general linear model. We show how to use the GaussianProcessFitter class, which estimates the parameters of the model.

import openturns as ot
import openturns.viewer as otv

We create a model and a sample from this model.

dimension = 2
input_names = ["x1", "x2"]
formulas = ["cos(0.1 * x1 + 0.2 * x2)"]
model = ot.SymbolicFunction(input_names, formulas)
distribution = ot.Normal(dimension)
x = distribution.getSample(100)
y = model(x)

We create a GaussianProcessFitter based on a quadratic basis. The run method estimates the coefficients of the trend and the hyperparameters of the covariance model.

basis = ot.QuadraticBasisFactory(dimension).build()
covarianceModel = ot.SquaredExponential([1] * dimension, [1.0])
algo = ot.GaussianProcessFitter(x, y, covarianceModel, basis)
algo.run()
result = algo.getResult()

We see that the trend coefficients have been estimated.

result.getTrendCoefficients()

class=Point name=Unnamed dimension=6 values=[0.989257,-9.12733e-05,-7.86187e-05,-0.00442874,-0.017767,-0.017804]

The parameters of the covariance models also have been estimated.

result.getCovarianceModel()

SquaredExponential(scale=[3.43738,1.84178], amplitude=[0.00436343])

The getMetaModel method returns the metamodel where the parameters have been estimated.

responseSurface = result.getMetaModel()

Plot the output of our model depending on with .

xmin = -5.0
xmax = 5.0
x1value = 0.5
parametricModelGraph = ot.ParametricFunction(model, [0], [x1value]).draw(xmin, xmax)
graphMetamodel = ot.ParametricFunction(responseSurface, [0], [x1value]).draw(xmin, xmax)
parametricModelGraph.add(graphMetamodel)
parametricModelGraph.setLegends(["Model", "Meta-Model"])
parametricModelGraph.setLegendPosition("upper right")
view = otv.View(parametricModelGraph)

view.ShowAll()