# [ot-users] Matern Covariance Model for Kriging Surrogate Model

LELIEVRE-Nicolas nicolas.lelievre at sigma-clermont.fr
Tue Jul 11 10:50:13 CEST 2017

Hi,

I want to calibrate a Kriging surrogate model in OpenTurns and I face difficulties.
Indeed, I want to use the Matern covariance model.
But, when I run the KrigingAlgorithm optimization, the scale parameters (theta) are not optimized.
I have studied the problem and found that the LogLikelihood function is constant, no matter how points are in the DoE, what the performance function is and what the dimension is.

I think that the problem is on the definition of the covariance model since if I use SquaredExponential there is not any problems.
But, I don't find how to define it correctly.

A little example:

import numpy as np
import openturns as ot
def G(X):
out = 15 - (X[:,0]**2 + X[:,1]**2 - 5*np.cos(2*np.pi*X[:,0]) - 5*np.cos(2*np.pi*X[:,1]))
return out

dim = 2
Loi = np.ones(dim)
Moy = np.ones(dim)
Stdev = np.ones(dim)
nini = 100

nva = np.size(Loi)
DOE_u = np.random.normal(0,1,(nini,nva))
DOE_y = G(DOE_u)
DOE_y = DOE_y.reshape((nini,1))

inputSample = ot.Sample(DOE_u)
outputSample = ot.Sample(DOE_y)
basis = ot.ConstantBasisFactory(nva).build()
covarianceModel = ot.MaternModel(nva)
covarianceModel.setNu(5/2)
algo = ot.KrigingAlgorithm(inputSample, outputSample, covarianceModel, basis)
algo.run()
result = algo.getResult()
print(result.getCovarianceModel())
LogLikelihood = algo.getReducedLogLikelihoodFunction()

Nicolas Lelièvre
Doctorant Institut Pascal Clermont-Ferrand

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