Reconstruction of wide spectrum forcing in transport-diffusion and Navier-Stokes equations
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916668440051712 |
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| author | Bröcker, Jochen Carigi, Giulia Kuna, Tobias Martinez, Vincent R. |
| author_facet | Bröcker, Jochen Carigi, Giulia Kuna, Tobias Martinez, Vincent R. |
| contents | This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics and various applications. Two algorithms are proposed to address this problem: one that iteratively reconstructs forcing and another that provides a continuous-time reconstruction. Convergence is shown to be guaranteed provided that observational resolution is sufficiently high and algorithmic parameters are properly tuned according to the prior information; these conditions are quantified precisely. The class of reconstructable forces identified here include those which are time-dependent and potentially inject energy at all length scales. This significantly expands upon the class of forces in previous studies, which could only accommodate those with band-limited spectra. The second algorithm moreover provides a conceptually streamlined approach that allows for a more straightforward analysis and simplified practical implementation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction of wide spectrum forcing in transport-diffusion and Navier-Stokes equations Bröcker, Jochen Carigi, Giulia Kuna, Tobias Martinez, Vincent R. Optimization and Control Analysis of PDEs 35Q30, 35B30, 93B30, 35R30, 76B75 This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinear setting that is paradigmatic in geophysical fluid dynamics and various applications. Two algorithms are proposed to address this problem: one that iteratively reconstructs forcing and another that provides a continuous-time reconstruction. Convergence is shown to be guaranteed provided that observational resolution is sufficiently high and algorithmic parameters are properly tuned according to the prior information; these conditions are quantified precisely. The class of reconstructable forces identified here include those which are time-dependent and potentially inject energy at all length scales. This significantly expands upon the class of forces in previous studies, which could only accommodate those with band-limited spectra. The second algorithm moreover provides a conceptually streamlined approach that allows for a more straightforward analysis and simplified practical implementation. |
| title | Reconstruction of wide spectrum forcing in transport-diffusion and Navier-Stokes equations |
| topic | Optimization and Control Analysis of PDEs 35Q30, 35B30, 93B30, 35R30, 76B75 |
| url | https://arxiv.org/abs/2504.00242 |