Cokriging-Based Sequential Design Strategies Using Fast Cross-Validation Techniques for Multi-Fidelity Computer Codes

Cokriging-based surrogate models have become popular in recent decades to approximate a computer code output from a few simulations using both coarse and more complex versions of the code. In practical applications, it is common to sequentially add new simulations to obtain more accurate approximations. We propose a method of cokriging-based sequential design, which combines both the error evaluation provided by the cokriging model and the observed errors of a leave-one-out cross-validation procedure. This method is proposed in two versions, the first one selects points one at a time. The second one allows us to parallelize the simulations and to add several design points at a time. The main advantage of the suggested strategies is that at a new design point they choose which code versions should be simulated (i.e., the complex code or one of its fast approximations). A multifidelity application is used to illustrate the efficiency of the proposed approaches. In this example, the accurate code is a two-dimensional finite element model and the less accurate one is a one-dimensional approximation of the system. This article has supplementary material online.