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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.14318 |
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| _version_ | 1866917873581031424 |
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| author | Sanz-Alonso, Daniel Waniorek, Nathan |
| author_facet | Sanz-Alonso, Daniel Waniorek, Nathan |
| contents | Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper establishes long-time accuracy of ensemble Kalman filters. We introduce conditions on the dynamics and the observations under which the estimation error remains small in the long-time horizon. Our theory covers a wide class of partially-observed chaotic dynamical systems, which includes the Navier-Stokes equations and Lorenz models. In addition, we prove long-time accuracy of ensemble Kalman filters with surrogate dynamics, thus validating the use of machine-learned forecast models in ensemble data assimilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems Sanz-Alonso, Daniel Waniorek, Nathan Dynamical Systems Numerical Analysis Machine Learning 62F15, 68Q25, 60G35, 62M05 Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper establishes long-time accuracy of ensemble Kalman filters. We introduce conditions on the dynamics and the observations under which the estimation error remains small in the long-time horizon. Our theory covers a wide class of partially-observed chaotic dynamical systems, which includes the Navier-Stokes equations and Lorenz models. In addition, we prove long-time accuracy of ensemble Kalman filters with surrogate dynamics, thus validating the use of machine-learned forecast models in ensemble data assimilation. |
| title | Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems |
| topic | Dynamical Systems Numerical Analysis Machine Learning 62F15, 68Q25, 60G35, 62M05 |
| url | https://arxiv.org/abs/2412.14318 |