An efficient method for goal-oriented linear Bayesian optimal experimental design: Application to optimal sensor placemen

TL;DR

This paper introduces an efficient goal-oriented Bayesian experimental design method that optimizes sensor placement to maximize information gain about a specific quantity of interest, especially in large-scale inverse problems.

Contribution

It develops a novel formula for expected information gain, leveraging low-rank structures and an online-offline scheme, enabling scalable sensor placement optimization.

Findings

The method achieves high accuracy in a contaminant transport inverse problem.

It is computationally efficient and independent of problem dimensions.

The approach effectively maximizes information gain for the QoI.

Abstract

Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data. In many applications, we seek to minimize the uncertainty of a predicted quantity of interest (QoI) based on the solution of the inverse problem, rather than the inversion model parameter itself. In these scenarios, we develop an efficient method for goal-oriented optimal experimental design (GOOED) for large-scale Bayesian linear inverse problem that finds sensor locations to maximize the expected information gain (EIG) for a predicted QoI. By deriving a new formula to compute the EIG, exploiting low-rank structures of two appropriate operators, we are able to employ an online-offline decomposition scheme and a swapping greedy algorithm to maximize the EIG at a cost measured in model solutions that is independent of the problem dimensions. We provide detailed error analysis of the approximated EIG, and demonstrate the efficiency, accuracy, and both data- and parameter-dimension independence of the proposed algorithm for a contaminant transport inverse problem with infinite-dimensional parameter field.