{"ID":2864929,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21751","arxiv_id":"2509.21751","title":"Reparameterizing 4DVAR with neural fields","abstract":"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.","short_abstract":"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 parameterize...","url_abs":"https://arxiv.org/abs/2509.21751","url_pdf":"https://arxiv.org/pdf/2509.21751v1","authors":"[\"Jaemin Oh\"]","published":"2025-09-26T01:30:33Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"physics.comp-ph\",\"physics.flu-dyn\"]","methods":"[]","has_code":false}