Numerical studies of the metamodel fitting and validation processes

TL;DR

This paper evaluates different space filling designs for Gaussian process metamodels and introduces an optimized validation algorithm to improve predictivity assessment with fewer validation points.

Contribution

It compares Latin hypercube designs based on discrepancy measures and proposes a new sequential validation method for better metamodel predictivity estimation.

Findings

Minimal wrap-around discrepancy samples enhance Gaussian process metamodel accuracy.

The proposed validation algorithm reduces the number of validation points needed.

Application to nuclear safety code demonstrates practical effectiveness.

Abstract

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.