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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2509.21751 |
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| _version_ | 1866918148322623488 |
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| author | Oh, Jaemin |
| author_facet | Oh, Jaemin |
| contents | Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, but its cost function is difficult to optimize and computationally intensive. We propose a neural field-based reformulation in which the full spatiotemporal state is represented as a continuous function parameterized by a neural network. This reparameterization removes the time-sequential dependency of classical 4DVAR, enabling parallel-in-time optimization in parameter space. Physical constraints are incorporated directly through a physics-informed loss, simplifying implementation and reducing computational cost. We evaluate the method on the two-dimensional incompressible Navier--Stokes equations with Kolmogorov forcing. Compared to a baseline 4DVAR implementation, the neural reparameterized variants produce more stable initial condition estimates without spurious oscillations. Notably, unlike most machine learning-based approaches, our framework does not require access to ground-truth states or reanalysis data, broadening its applicability to settings with limited reference information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21751 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reparameterizing 4DVAR with neural fields Oh, Jaemin Machine Learning Computational Physics Fluid Dynamics Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, but its cost function is difficult to optimize and computationally intensive. We propose a neural field-based reformulation in which the full spatiotemporal state is represented as a continuous function parameterized by a neural network. This reparameterization removes the time-sequential dependency of classical 4DVAR, enabling parallel-in-time optimization in parameter space. Physical constraints are incorporated directly through a physics-informed loss, simplifying implementation and reducing computational cost. We evaluate the method on the two-dimensional incompressible Navier--Stokes equations with Kolmogorov forcing. Compared to a baseline 4DVAR implementation, the neural reparameterized variants produce more stable initial condition estimates without spurious oscillations. Notably, unlike most machine learning-based approaches, our framework does not require access to ground-truth states or reanalysis data, broadening its applicability to settings with limited reference information. |
| title | Reparameterizing 4DVAR with neural fields |
| topic | Machine Learning Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2509.21751 |