FEM-based A-optimal sensor placement for heat source inversion from final time measurement
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912604045180928 |
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| author | Aarset, Christian Nguyen, Tram Thi Ngoc |
| author_facet | Aarset, Christian Nguyen, Tram Thi Ngoc |
| contents | Within the field of optimal experimental design, \emph{sensor placement} refers to the act of finding the optimal locations of data collecting sensors, with the aim to optimise reconstruction of an unknown parameter from finite data. In this work, we investigate sensor placement for the inverse problem of reconstructing a heat source given final time measurements. Employing forward and adjoint analysis of this PDE-driven model, we show how one can leverage the first author's recently invented \emph{redundant-dominant $p$-continuation} algorithm to obtain binary A-optimal sensor placements also for this time-dependent model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19679 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FEM-based A-optimal sensor placement for heat source inversion from final time measurement Aarset, Christian Nguyen, Tram Thi Ngoc Optimization and Control 62K05, 62F15, 35R30, 65K10, 90C25, 90C26, 35K05 Within the field of optimal experimental design, \emph{sensor placement} refers to the act of finding the optimal locations of data collecting sensors, with the aim to optimise reconstruction of an unknown parameter from finite data. In this work, we investigate sensor placement for the inverse problem of reconstructing a heat source given final time measurements. Employing forward and adjoint analysis of this PDE-driven model, we show how one can leverage the first author's recently invented \emph{redundant-dominant $p$-continuation} algorithm to obtain binary A-optimal sensor placements also for this time-dependent model. |
| title | FEM-based A-optimal sensor placement for heat source inversion from final time measurement |
| topic | Optimization and Control 62K05, 62F15, 35R30, 65K10, 90C25, 90C26, 35K05 |
| url | https://arxiv.org/abs/2509.19679 |