Kriging and Computer Experiments

Engineering problems where complex computer codes need to be run in order to obtain a solution are increasingly common. This could be, for example, a finite-element program which evaluates certain physical properties of a mechanical design. The finite element model is accurate and deterministic in the sense that when run from the same settings it produces the exact same outputs, but may take a long time to run. Still, a faster approximation (or metamodel) of the computer code output is desirable, particularly for optimization purposes, since optimization would require running the code several times. The accuracy (bias) of such approximation is of prime interest. This leads to a different problem of function approximation methods, closer to what Chebyshev investigated in the XIX century. Kriging methods are one class of popular methods to provide interpolation of complex, “expensive” functions which can only be observed by running such a computer code. This chapter provides an introduction to Kriging methods used for prediction. We also discuss experimental design issues for computer codes, in particular, space filling designs used to reduce bias in the fitted model.