Optimal Experimental Design for Infinite-dimensional Bayesian Inverse Problems Governed by PDEs: A Review

TL;DR

This review discusses optimal experimental design methods for infinite-dimensional Bayesian inverse problems governed by PDEs, focusing on measurement placement to minimize parameter uncertainty and surveying computational approaches.

Contribution

It provides a comprehensive overview of mathematical foundations and computational methods for OED in PDE-governed Bayesian inverse problems with infinite-dimensional parameters.

Findings

Survey of existing computational methods

Discussion of mathematical foundations

Identification of future research directions

Abstract

We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the placement of measurement points, at which data are collected, such that the uncertainty in the estimated parameters is minimized. We present the mathematical foundations of OED in this context and survey the computational methods for the class of OED problems under study. We also outline some directions for future research in this area.