A Dynamical Neural Galerkin Scheme for Filtering Problems
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911768365760512 |
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| author | Aghili, Joubine Atokple, Joy Zialesi Billaud-Friess, Marie Garnier, Guillaume Mula, Olga Tognon, Norbert |
| author_facet | Aghili, Joubine Atokple, Joy Zialesi Billaud-Friess, Marie Garnier, Guillaume Mula, Olga Tognon, Norbert |
| contents | This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model with unknown parameters. We present a filtering algorithm where the reconstruction of the dynamics is done with neural network approximations whose weights are dynamically updated using observational data. In addition to the estimate of the state, we also obtain time-dependent parameter estimations of the PDE parameters governing the observed evolution. We illustrate the behavior of the method in a one-dimensional KdV equation involving the transport of solutions with local support. Our numerical investigation reveals the importance of the location and number of the observations. In particular, it suggests to consider dynamical sensor placement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Dynamical Neural Galerkin Scheme for Filtering Problems Aghili, Joubine Atokple, Joy Zialesi Billaud-Friess, Marie Garnier, Guillaume Mula, Olga Tognon, Norbert Numerical Analysis This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model with unknown parameters. We present a filtering algorithm where the reconstruction of the dynamics is done with neural network approximations whose weights are dynamically updated using observational data. In addition to the estimate of the state, we also obtain time-dependent parameter estimations of the PDE parameters governing the observed evolution. We illustrate the behavior of the method in a one-dimensional KdV equation involving the transport of solutions with local support. Our numerical investigation reveals the importance of the location and number of the observations. In particular, it suggests to consider dynamical sensor placement. |
| title | A Dynamical Neural Galerkin Scheme for Filtering Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.17748 |