Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

Abstract

Inferring arbitrary quantities of interest (QoI) using limited computational or, in realistic scenarios, financial budgets, is a challenging problem that requires sophisticated strategies for the optimal allocation of the available resources. Bayesian optimal experimental design identifies the optimal set of design locations for the purpose of solving a parameter inference problem and the optimality criterion is typically associated with maximizing the worth of information in the experimental measurements. Sequential design strategies further identify the optimal design in a sequential manner, starting from a initial budget and iteratively selecting new optimal points until either an accuracy threshold is reached, or a cost limit is exceeded. In this paper, we present a generic sequential Bayesian experimental design framework that relies on maximizing an information theoretic design criterion, namely the Expected Information Gain, in order to infer QoIs formed as nonlinear operators acting on black-box functions. Our framework relies on modeling the underlying response function using non-stationary Gaussian Processes, thus enabling efficient sampling from the QoI in order to provide Monte Carlo estimators for the design criterion. We demonstrate the performance of our method on an engineering problem of steel wire manufacturing and compare it with two classic approaches: uncertainty sampling and expected improvement.