Numerical studies of the metamodel fitting and validation processes. (arXiv:1001.1049v1 [math.NA])

Complex computer codes, for instance simulating physical phenomena, are often
too time expensive to be directly used to perform uncertainty, sensitivity,
optimization and robustness analyses. A widely accepted method to circumvent
this problem consists in replacing cpu time expensive computer models by cpu
inexpensive mathematical functions, called metamodels. In this paper, we focus
on the Gaussian process metamodel and two essential steps of its definition
phase. First, the initial design of the computer code input variables (which
allows to fit the metamodel) has to honor adequate space filling properties. We
adopt a numerical approach to compare the performance of different types of
space filling designs, in the class of the optimal Latin hypercube samples, in
terms of the predictivity of the subsequent fitted metamodel. We conclude that
such samples with minimal wrap-around discrepancy are particularly well-suited
for the Gaussian process metamodel fitting. Second, the metamodel validation
process consists in evaluating the metamodel predictivity with respect to the
initial computer code. We propose and test an algorithm which optimizes the
distance between the validation points and the metamodel learning points in
order to estimate the true metamodel predictivity with a minimum number of
validation points. Comparisons with classical validation algorithms and
application to a nuclear safety computer code show the relevance of this new
sequential validation design.

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Original source : http://arxiv.org/abs/1001.1049...