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"""
Validate a polynomial chaos
===========================
"""
# %%
#
# In this example, we show how to perform the validation plot of a polynomial chaos for the :ref:`Ishigami function <use-case-ishigami>`.
# %%
from openturns.usecases import ishigami_function
import openturns as ot
import openturns.viewer as otv
# %%
# Model description
# -----------------
# %%
# We load the Ishigami test function from the usecases module :
im = ishigami_function.IshigamiModel()
# %%
# The model contains the input distribution :math:`X=(X_1, X_2, X_3)` in
# `im.distribution` and the Ishigami function in `im.model`.
# We also have access to the input variable names with
input_names = im.distribution.getDescription()
# %%
N = 100
inputTrain = im.distribution.getSample(N)
outputTrain = im.model(inputTrain)
# %%
# Create the chaos
# ----------------
# %%
# We could use only the input and output training samples: in this case, the distribution of the input sample is computed by selecting the best distribution that fits the data.
# %%
chaosalgo = ot.FunctionalChaosAlgorithm(inputTrain, outputTrain)
# %%
# Since the input distribution is known in our particular case,
# we instead create the multivariate basis from the distribution,
# that is three independent variables :math:`X_1` , :math:`X_2` and :math:`X_3` .
# %%
multivariateBasis = ot.OrthogonalProductPolynomialFactory([im.X1, im.X2, im.X3])
totalDegree = 8
enumfunc = multivariateBasis.getEnumerateFunction()
basisSize = enumfunc.getBasisSizeFromTotalDegree(totalDegree)
adaptiveStrategy = ot.FixedStrategy(multivariateBasis, basisSize)
# %%
selectionAlgorithm = ot.LeastSquaresMetaModelSelectionFactory()
projectionStrategy = ot.LeastSquaresStrategy(
inputTrain, outputTrain, selectionAlgorithm
)
# %%
chaosalgo = ot.FunctionalChaosAlgorithm(
inputTrain, outputTrain, im.distribution, adaptiveStrategy, projectionStrategy
)
# %%
chaosalgo.run()
result = chaosalgo.getResult()
metamodel = result.getMetaModel()
# %%
# Validation of the metamodel
# ---------------------------
# %%
# In order to validate the metamodel, we generate a test sample.
# %%
n_valid = 1000
inputTest = im.distribution.getSample(n_valid)
outputTest = im.model(inputTest)
metamodelPredictions = metamodel(inputTest)
val = ot.MetaModelValidation(outputTest, metamodelPredictions)
r2Score = val.computeR2Score()[0]
r2Score
# %%
# The :math:`R^2` is very close to 1: the metamodel seems very accurate.
# %%
graph = val.drawValidation()
graph.setTitle("R2=%.2f%%" % (r2Score * 100))
view = otv.View(graph)
# %%
# The metamodel has a good predictivity, since the points are almost on the first diagonal.
# %%
# Display all figures
otv.View.ShowAll()
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