Adaptive numerical designs for the calibration of computer models

Making good predictions about a physical system using a computer model requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters, are specific to the computer model and most often uncertain. The goal of statistical calibration consists in tuning these parameters to make the outputs of the computer model as close as possible to the field measures. Where prior information is available, Bayesian inference can be conducted using MCMC methods, which are unfortunately unfeasible when the simulations are too time-consuming. A way to circumvent this issue is to emulate the computer model with a Gaussian process emulator. Using such a cheap approximation in the calibration process causes a new source of uncertainty which strongly depends on the choice of a numerical design of experiments from which this emulator is fitted. This uncertainty can be reduced by building a proper sequential design which is adapted to the calibration goal using the Expected Improvement criterion. Numerical illustrations in several dimensions are provided to assess the efficiency of such sequential strategies.