Optimal Bayesian experimental design for subsurface flow problems

TL;DR

This paper introduces a polynomial chaos expansion surrogate model to efficiently compute the expected information gain in Bayesian experimental design for subsurface flow, significantly reducing computational costs.

Contribution

The paper presents a novel PCE-based method to approximate the design utility function, replacing costly integrations with direct PCE construction, enabling efficient Bayesian experimental design.

Findings

PCE surrogate reduces computational cost of design optimization.

Method accurately approximates expected information gain.

Applicable to complex subsurface flow problems.

Abstract

Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of possible observations and determine an experimental setup that produces maximum information about the system parameters on average. Generally, optimal Bayesian design formulations result in multiple high-dimensional integrals that are difficult to evaluate without incurring significant computational costs as each integration point corresponds to solving a coupled system of partial differential equations. In the present work, we propose a novel approach for development of polynomial chaos expansion (PCE) surrogate model for the design utility function. In particular, we demonstrate how the orthogonality of PCE basis polynomials can be utilized in order to replace the expensive integration over the space of possible observations by direct construction of PCE approximation for the expected information gain. This novel technique enables the derivation of a reasonable quality response surface for the targeted objective function with a computational budget comparable to several single-point evaluations. Therefore, the proposed technique reduces dramatically the overall cost of optimal Bayesian experimental design. We evaluate this alternative formulation utilizing PCE on few numerical test cases with various levels of complexity to illustrate the computational advantages of the proposed approach.