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Kriging-based surrogate models have become very popular during the lastdecades to approximate a computer code output from few simulations. Inpractical applications, it is very common to sequentially add new simulationsto obtain more accurate approximations. We propose in this paper a method ofkriging-based sequential design which combines both the error evaluationproviding by the kriging model and the observed errors of a Leave-One-Outcross-validation procedure. This method is proposed in two versions, the firstone selects points one at-a-time. The second one allows us to parallelize thesimulations and to add several design points at-a-time. Then, we extend thesestrategies to multi-fidelity co-kriging models which allow us to surrogate acomplex code using fast approximations of it. The main advantage of theseextensions is that it not only provides the new locations where to performsimulations but also which versions of code have to be simulated (between thecomplex one or one of its fast approximations). A real multi-fidelityapplication is used to illustrate the efficiency of the proposed approaches. Inthis example, the accurate code is a two-dimensional finite element model andthe less accurate one is a one-dimensional approximation of the system.

Kriging-based sequential design strategies using fast cross-validation techniques with extensions to multi-fidelity computer codes