Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management
Numerical Analysis
2025-07-09 v2 Numerical Analysis
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.
Cite
@article{arxiv.2507.02500,
title = {Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management},
author = {Marco Mattuschka and Noah An der Lan and Max von Danwitz and Daniel Wolff and Alexander Popp},
journal= {arXiv preprint arXiv:2507.02500},
year = {2025}
}