ENBIS: European Network for Business and Industrial Statistics

Linear transformation on kernels for constraining Gaussian processes

21 September 2009, 16:05 – 16:25

Abstract

Submitted by

Nicolas Durrande

Authors

N. Durrande, B. Gauthier, O. Roustant

Affiliation

EMSE

Abstract

Gaussian processes are often used as a surrogate model to the response of costly simulators. In most cases, those processes are conditioned on a set of data in order to interpolate the response function on the design points. However numerical simulators sometimes have particular properties such as symmetries, known values of the derivative, being equal to a constant on some subvector space, etc. Classical meta-models cannot account for such kind of information which results in a great loss of accuracy of the model. However when linear transformations allow the images of the original process realisations to verify the desired properties, it is possible to calculate new kernels from the old one that would generate processes respecting those properties. We will pay a particular attention to the choice of those transformations since they have a great impact on the regularity of the new process. The method is illustrated on one and two dimension examples.

It would be interesting to present this talk just before the talk of B. Gauthier untitled “Kriging models including functional information”.

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