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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014006914
pages 365-386

RECURSIVE CO-KRIGING MODEL FOR DESIGN OF COMPUTER EXPERIMENTS WITH MULTIPLE LEVELS OF FIDELITY

Loic Le Gratiet
University Paris Diderot 75205 Paris Cedex 13, CEA, DAM, DIF, F-91297 Arpajon, France
Josselin Garnier
Laboratoire de Probabilites et Modeles Aleatoires & Laboratoire Jacques-Louis Lions, Universite Paris Diderot, 75205 Paris Cedex 13, France

ABSTRACT

We consider in this paper the problem of building a fast-running approximation−also called surrogate model−of a complex computer code. The co-kriging based surrogate model is a promising tool to build such an approximation when the complex computer code can be run at different levels of accuracy. We present here an original approach to perform a multi-fidelity co-kriging model which is based on a recursive formulation. We prove that the predictive mean and the variance of the presented approach are identical to the ones of the original co-kriging model. However, our new approach allows to obtain original results. First, closed-form formulas for the universal co-kriging predictive mean and variance are given. Second, a fast cross-validation procedure for the multi-fidelity co-kriging model is introduced. Finally, the proposed approach has a reduced computational complexity compared to the previous one. The multi-fidelity model is successfully applied to emulate a hydrodynamic simulator.