NDLI: Efficient D-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Alexanderian, Alen Saibaba, Arvind K.
Copyright Year	2018
Abstract	We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the infinite-dimensional limit. The optimal design is obtained by solving an optimization problem that involves repeated evaluation of the log-determinant of high-dimensional operators along with their derivatives. Forming and manipulating these operators is computationally prohibitive for large-scale problems. Our methods exploit the low-rank structure in the inverse problem in three different ways, yielding efficient algorithms. Specifically, we propose three approaches for computing the D-optimal criterion, its gradient, and the Kullback--Leibler (KL) divergence from the posterior to prior. The first approach is based on truncated spectral decomposition of the prior-preconditioned data misfit Hessian, the second approach uses randomized matrix methods, and the third approach uses a fixed low-rank approximation of the prior-preconditioned forward operator. Detailed error analysis is provided for each of the methods, and their effectiveness is demonstrated on a model sensor placement problem for initial state reconstruction in a time-dependent advection-diffusion equation in two space dimensions.
Sponsorship	National Science Foundation
Starting Page	A2956
Ending Page	A2985
Page Count	30
File Format	PDF
ISSN	10648275
DOI	10.1137/17M115712X
e-ISSN	10957197
Issue Number	5
Volume Number	40
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-13
Access Restriction	Subscribed
Subject Keyword	uncertainty quantification large-scale ill-posed inverse problems Inverse problems Bayesian inversion Computational problems in statistics Optimal designs Randomized algorithms PDEs in connection with statistics D-optimal experimental design low-rank approximation Bayesian inference randomized matrix methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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