A Greedy Sensor Selection Algorithm for Hyperparameterized Linear Bayesian Inverse Problems

TL;DR

This paper introduces a greedy sensor selection algorithm for linear Bayesian inverse problems with hyper-parameters, enabling optimal sensor placement across multiple configurations while accounting for correlated noise and high-dimensional models.

Contribution

It proposes a novel greedy algorithm that improves sensor placement for hyper-parameterized inverse problems, incorporating correlated noise and model reduction for scalability.

Findings

Effective sensor placement across configurations demonstrated on geophysical models

Algorithm handles correlated noise in large candidate sets

Scalable to high-dimensional models with model order reduction

Abstract

We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed physical system. To optimally reduce the uncertainty in the system's model with a single set of sensors, the initial sensor placement needs to account for the non-linear state changes of all admissible configurations. We address this requirement through an observability coefficient which links the posteriors' uncertainties directly to the choice of sensors. We propose a greedy sensor selection algorithm to iteratively improve the observability coefficient for all configurations through orthogonal matching pursuit. The algorithm allows explicitly correlated noise models even for large sets of candidate sensors, and remains computationally efficient for high-dimensional forward models through model order reduction. We demonstrate our approach on a large-scale geophysical model of the Perth Basin, and provide numerical studies regarding optimality and scalability with regard to classic optimal experimental design utility functions.