Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908439770300416 |
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| author | Mattuschka, Marco der Lan, Noah An von Danwitz, Max Wolff, Daniel Popp, Alexander |
| author_facet | Mattuschka, Marco der Lan, Noah An von Danwitz, Max Wolff, Daniel Popp, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management Mattuschka, Marco der Lan, Noah An von Danwitz, Max Wolff, Daniel Popp, Alexander Numerical Analysis 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. |
| title | Goal-oriented optimal sensor placement for PDE-constrained inverse problems in crisis management |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.02500 |