期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 42, 期 3, 页码 A1714-A1740出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1267362
关键词
Bayesian inversion; A-optimal experimental design; large-scale ill-posed inverse problems; randomized matrix methods; reweighted l(1) minimization; uncertainty quantification
资金
- NSF [DMS-1745654]
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the posterior covariance operator. We propose using structure exploiting randomized methods to compute the A-optimal objective function and its gradient, and we provide a detailed analysis of the error for the proposed estimators. To ensure sparse and binary design vectors, we develop a novel reweighted l(1)-minimization algorithm. We also introduce a modified A-optimal criterion and present randomized estimators for its efficient computation. We present numerical results illustrating the proposed methods on a model contaminant source identification problem, where the inverse problem seeks to recover the initial state of a contaminant plume using discrete measurements of the contaminant in space and time.
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