Gaussian field models for the adaptive design of costly experiments

Résumé

Gaussian field models have become commonplace in the design and analysis of costly experiments. Thanks to convenient properties of associated conditional distributions (Gaussianity, interpolation in the case of deterministic responses, etc.), Gaussian field models not only allow predicting black-box responses for untried input configurations, but can also be used as a basis for evaluation strategies dedicated to optimization, inversion, uncertainty quantification, probability of failure estimation, and more. After an introduction to Gaussian field modeling and some of its popular applications in adaptive design of deterministic numerical experiments, we will present two recent contributions. First, results on infill sampling criteria for uncertainty reduction will be presented and illustrated, with application to an excursion set estimation problem from safety engineering. Second, we will focus on a high-dimensional application of Gaussian field modeling to an inversion problem in water sciences, where an original non-stationary covariance kernel relying on fast proxy simulations is used.