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In many practical cases, a sensitivity analysis or an optimization of acomplex time consuming computer code requires to build a fast runningapproximation of it - also called surrogate model. We consider in this paperthe problem of building a surrogate model of a complex computer code which canbe run at different levels of accuracy. The co-kriging based surrogate model isa promising tool to build such an approximation. The idea is to improve thesurrogate model by using fast and less accurate versions of the code. Wepresent here a new approach to perform a multi-fidelity co-kriging model whichis based on a recursive formulation. The strength of this new method is thatthe co-kriging model is built through a series of independent kriging models.From them, some properties of classical kriging models can naturally beextended to the presented co-kriging model such as a fast cross-validationprocedure. Moreover, based on a Bayes linear formulation, an extension of theuniversal kriging equations are provided for the co-kriging model. Finally, theproposed model has the advantage to reduce the computational complexitycompared to the previous models. The multi-fidelity model is successfullyapplied to emulate a hydrodynamic simulator. This real example illustrates theefficiency of the recursive model.

Recursive co-kriging model for Design of Computer experiments with multiple levels of fidelity with an application to hydrodynamic