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Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Summary: Stepwise uncertainty reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. This article introduces several multipoint sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. The authors also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. The performance of these strategies is illustrated in various numerical experiments, including a nuclear safety test case. Basic explanations about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

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  • Topics: Design of Experiments
  • Keywords: Kriging, Uncertainty, Stepwise procedures, Batch processes, Sequential methods, Design of experiments (DOE), Gaussian curve
  • Author: Chevalier, Clément; Ginsbourger, David; Bect, Julien; Vazquez, Emmanuel; Picheny, Victor; Richet, Yann;
  • Journal: Technometrics