Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set

Chevalier, Clément; Bect, Julien; Ginsbourger, David; Vazquez, Emmanuel; Picheny, Victor; Richet, Yann (2014). Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set. Technometrics, 56(4), pp. 455-465. Taylor & Francis 10.1080/00401706.2013.860918

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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. In this article we introduce 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. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code, and data are available online as supplementary materials.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Chevalier, Clément and Ginsbourger, David

Subjects:

500 Science > 510 Mathematics

ISSN:

0040-1706

Publisher:

Taylor & Francis

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

12 Dec 2014 12:02

Last Modified:

20 Jan 2016 14:36

Publisher DOI:

10.1080/00401706.2013.860918

BORIS DOI:

10.7892/boris.60982

URI:

https://boris.unibe.ch/id/eprint/60982

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