2017/11/15 by Alen Alexanderian, Arvind K. Saibaba, Alexanderian, Alen +1 · 3 citations
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1711.05878
openalex publication_date 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a computational framework for D-optimal experimental design for\nPDE-based Bayesian linear inverse problems with infinite-dimensional\nparameters. We follow a formulation of the experimental design problem that\nremains valid in the infinite-dimensional limit. The optimal design is obtained\nby solving an optimization problem that involves repeated evaluation of the\nlog-determinant of high-dimensional operators along with their derivatives.\nForming and manipulating these operators is computationally prohibitive for\nlarge-scale problems. Our methods exploit the low-rank structure in the inverse\nproblem in three different ways, yielding efficient algorithms. Our main\napproach is to use randomized estimators for computing the D-optimal criterion,\nits derivative, as well as the Kullback--Leibler divergence from posterior to\nprior. Two other alternatives are proposed based on a low-rank approximation of\nthe prior-preconditioned data misfit Hessian, and a fixed low-rank\napproximation of the prior-preconditioned forward operator. Detailed error\nanalysis is provided for each of the methods, and their effectiveness is\ndemonstrated on a model sensor placement problem for initial state\nreconstruction in a time-dependent advection-diffusion equation in two space\ndimensions.\n