Reparameterizing 4DVAR with neural fields

• URL: http://arxiv.org/abs/2509.21751v1
• Date: Fri, 26 Sep 2025 01:30:33 GMT
• Title: Reparameterizing 4DVAR with neural fields
• Authors: Jaemin Oh,
• Abstract summary: We propose a neural field-based implementation in which the full state is represented as a continuous function parameterized by a neural network.<n>We evaluate the method on the two-dimensional incompressible Navier--Stokes equations with Kolmogorov forcing.<n>Unlike most machine learning-based approaches, our framework does not require access to ground-truth states or reanalysis data.
• Score: 1.4721615285883427
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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