# On the Effect of Neural Field Reparameterization for 4DVAR

arXiv: https://arxiv.org/abs/2509.21751 · HTML: https://mlsanity.com/paper/2509.21751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
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- [Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.15969/) (2023)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representations](https://mlsanity.com/paper/2412.05994/) (2024)
- [Controlling diverse robots by inferring Jacobian fields with deep networks](https://mlsanity.com/paper/2407.08722/) (2024)
- [Latent assimilation with implicit neural representations for unknown dynamics](https://mlsanity.com/paper/2309.09574/) (2023)
- [Accurate deep learning-based filtering for chaotic dynamics by identifying instabilities without an ensemble](https://mlsanity.com/paper/2408.04739/) (2024)
- [Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation](https://mlsanity.com/paper/2501.13312/) (2025)
- [High performance Python for direct numerical simulations of turbulent flows](https://mlsanity.com/paper/1602.03638/) (2016)
- [Neural Operator-Based Nonlinear Nudging for Chaotic Dynamical Systems](https://mlsanity.com/paper/2508.05778/) (2025)

## Abstract (arXiv)

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.