Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review. (1st March 2021)

• Record Type: Journal Article
• Authors: Alexanderian, Alen
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-01
• Subjects: optimal experimental design -- inverse problem -- Bayesian inference in Hilbert space -- sensor placement; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abe10c
• Languages: English
• ISSNs: 0266-5611

Abstract

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.