On the Effect of Neural Field Reparameterization for 4DVAR

Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, yet it remains computationally intensive and sensitive to initialization due to the non-convexity of its objective function. We propose a neural field-based reformulation of 4DVAR in which the spatiotemporal state is represented as a continuous function parameterized by a neural network. We demonstrate that optimizing in parameter space leverages the spectral bias of neural fields, acting as an implicit regularizer that stabilizes state estimation and suppresses spurious high-frequency oscillations without requiring explicit background error covariance information. Furthermore, by parameterizing the full spatiotemporal trajectory, our framework enables parallel-in-time optimization and incorporates physical constraints directly through physics-informed losses. Evaluations on chaotic benchmarks, including 2D Kolmogorov flow and 3D Taylor-Green vortices, show that neural reparameterization produces more accurate initial conditions than classical 4DVAR. When combined with separable neural architectures (SPINNs), the method achieves substantial speedups. Unlike many machine learning approaches, this framework requires no ground-truth training data, offering a robust and scalable alternative for operational data assimilation.