Adaptive numerical designs for the calibration of computer codes

Abstract: Making good predictions of a physical system using a computer code 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 code and most often uncertain. The goal of statistical calibration consists in estimating these parameters with the help of a statistical model which links the code outputs with the field measurements. In a Bayesian setting, the posterior distribution of these parameters is normally sampled using MCMC methods. However, they are impractical when the code runs are high time-consuming. A way to circumvent this issue consists of replacing the computer code with a Gaussian process emulator, then sampling a cheap-to-evaluate posterior distribution based on it. Doing so, calibration is subject to an error which strongly depends on the numerical design of experiments used to fit the emulator. We aim at reducing this error by building a proper sequential design by means of the Expected Improvement criterion. Numerical illustrations in several dimensions assess the efficiency of such sequential strategies.