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

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Authors

  • Marco Mattuschka Institute for the Protection of Terrestrial Infrastructures, German Aerospace Center (DLR), Sankt Augustin, Germany ORCID ID 0009-0009-6325-3578
  • Noah An der Lan Institute for the Protection of Terrestrial Infrastructures, German Aerospace Center (DLR), Sankt Augustin, Germany
  • Max von Danwitz Institute for the Protection of Terrestrial Infrastructures, German Aerospace Center (DLR), Sankt Augustin, Germany ORCID ID 0000-0002-2814-0027
  • Daniel Wolff Institute for Mathematics and Computer-Based Simulation (IMCS), University of the Bundeswehr Munich, Neubiberg, Germany ORCID ID 0000-0001-5767-7803
  • Popp Alexander 1) Institute for the Protection of Terrestrial Infrastructures, German Aerospace Center (DLR), Sankt Augustin; 2) Institute for Mathematics and Computer-Based Simulation (IMCS), University of the Bundeswehr Munich, Neubiberg, Germany ORCID ID 0000-0002-8820-466X

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.

Keywords:

Airborne contaminant transport , Advection-diffusion equation, Large-scale inverse problems, Optimal experimental design, Dynamic sensor steering