Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management

TL;DR

This paper introduces a Bayesian framework for goal-oriented optimal sensor placement and steering in PDE-constrained inverse problems, enhancing real-time crisis management through efficient, geometry-adapted strategies validated by numerical experiments.

Contribution

It develops a novel Bayesian, low-rank approximation-based framework for static and dynamic sensor placement in complex PDE problems, extending existing methods to real-time crisis scenarios.

Findings

Effective sensor placement reduces uncertainty in source identification.

Framework achieves computational efficiency with low-rank approximations.

Numerical experiments demonstrate practical applicability in crisis management.

Abstract

This paper presents a novel framework for goal-oriented optimal static sensor placement and dynamic sensor steering in PDE-constrained inverse problems, utilizing a Bayesian approach accelerated by low-rank approximations. The framework is applied to airborne contaminant tracking, extending recent dynamic sensor steering methods to complex geometries for computational efficiency. A C-optimal design criterion is employed to strategically place sensors, minimizing uncertainty in predictions. Numerical experiments validate the approach's effectiveness for source identification and monitoring, highlighting its potential for real-time decision-making in crisis management scenarios.