Data assimilation via model reference adaptation for linear and nonlinear dynamical systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| author | Kaltenbach, Benedikt Aarset, Christian Nguyen, Tram Thi Ngoc |
| author_facet | Kaltenbach, Benedikt Aarset, Christian Nguyen, Tram Thi Ngoc |
| contents | We address data assimilation for linear and nonlinear dynamical systems via the so-called \emph{model reference adaptive system}. Continuing our theoretical developments in \cite{Tram_Kaltenbacher_2021}, we deliver the first practical implementation of this approach for online parameter identification with time series data. Our semi-implicit scheme couples a modified state equation with a parameter evolution law that is driven by model-data residuals. We demonstrate four benchmark problems of increasing complexity: the Darcy flow, the Fisher-KPP equation, a nonlinear potential equation and finally, an Allen-Cahn type equation. Across all cases, explicit model reference adaptive system construction, verified assumptions and numerically stable reconstructions underline our proposed method as a reliable, versatile tool for data assimilation and real-time inversion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10920 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data assimilation via model reference adaptation for linear and nonlinear dynamical systems Kaltenbach, Benedikt Aarset, Christian Nguyen, Tram Thi Ngoc Optimization and Control Analysis of PDEs Dynamical Systems 65M32, 65J22, 35R30 We address data assimilation for linear and nonlinear dynamical systems via the so-called \emph{model reference adaptive system}. Continuing our theoretical developments in \cite{Tram_Kaltenbacher_2021}, we deliver the first practical implementation of this approach for online parameter identification with time series data. Our semi-implicit scheme couples a modified state equation with a parameter evolution law that is driven by model-data residuals. We demonstrate four benchmark problems of increasing complexity: the Darcy flow, the Fisher-KPP equation, a nonlinear potential equation and finally, an Allen-Cahn type equation. Across all cases, explicit model reference adaptive system construction, verified assumptions and numerically stable reconstructions underline our proposed method as a reliable, versatile tool for data assimilation and real-time inversion. |
| title | Data assimilation via model reference adaptation for linear and nonlinear dynamical systems |
| topic | Optimization and Control Analysis of PDEs Dynamical Systems 65M32, 65J22, 35R30 |
| url | https://arxiv.org/abs/2602.10920 |