Bayesian D-Optimal Experimental Designs via Column Subset Selection

Abstract. This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general optimal experimental design (OED) problem, using the D-optimality criterion. This is done by establishing connections between sensor placement and the column subset selection problem (CSSP), which is a well-studied problem in numerical linear algebra (NLA). In particular, we use the Golub–Klema–Stewart (GKS) approach, which involves computing the truncated singular value decomposition (SVD) followed by a pivoted QR factorization on the right singular vectors. The algorithms are further accelerated by using randomization to compute the low-rank approximation as well as for sampling the indices. The resulting algorithms are robust, computationally efficient, amenable to parallelization, require virtually no parameter tuning, and come with strong theoretical guarantees. One of the proposed algorithms is also adjoint-free, which is beneficial in situations where the adjoint is expensive to evaluate or is not available. Additionally, we develop a method for data completion without solving the inverse problem. Numerical experiments on model inverse problems involving the heat equation and seismic tomography in two spatial dimensions demonstrate the performance of our approaches. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and Data Available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/RandomizedOED/css4oed and in the supplementary materials ( M164986_Supplementary_Materials_2.pdf [455KB], css4oed-main.zip [820KB]). [Formula: see text]