Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management (2507.02500v1)

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.