Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909702851395584 |
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| author | Lu, Jingcheng Qi, Kunlun Wang, Li Calder, Jeff |
| author_facet | Lu, Jingcheng Qi, Kunlun Wang, Li Calder, Jeff |
| contents | Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based nudging system coupled with a novel discretization technique. This approach facilitates the simultaneous recovery of both the force term and a high-resolution solution from sparsely observed data. To address potential numerical artifacts, we use kernel regression to fit the observed data. We also analyze the convergence of the proposed nudging system under both full and partial data scenarios. When applied to moment systems, the source term involves the derivative of higher-order moments, our approach serves as a crucial step for data preparation in machine-learning based moment closure models. Multiple numerical experiments demonstrate the effectiveness of our algorithm, and we discuss its potential extension to high-dimensional systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03872 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery Lu, Jingcheng Qi, Kunlun Wang, Li Calder, Jeff Numerical Analysis 93C20, 70S10, 65Dxx, 42A15, 82C40 Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based nudging system coupled with a novel discretization technique. This approach facilitates the simultaneous recovery of both the force term and a high-resolution solution from sparsely observed data. To address potential numerical artifacts, we use kernel regression to fit the observed data. We also analyze the convergence of the proposed nudging system under both full and partial data scenarios. When applied to moment systems, the source term involves the derivative of higher-order moments, our approach serves as a crucial step for data preparation in machine-learning based moment closure models. Multiple numerical experiments demonstrate the effectiveness of our algorithm, and we discuss its potential extension to high-dimensional systems. |
| title | Continuous data assimilation for hydrodynamics: consistent discretization and application to moment recovery |
| topic | Numerical Analysis 93C20, 70S10, 65Dxx, 42A15, 82C40 |
| url | https://arxiv.org/abs/2409.03872 |