PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems

TL;DR

PhyDA is a novel physics-guided diffusion model that improves atmospheric data assimilation by ensuring physical consistency and handling observational sparsity, outperforming existing data-driven methods.

Contribution

Introduces PhyDA, a diffusion framework incorporating physical constraints and a virtual encoder for more accurate, physically consistent atmospheric data reconstruction.

Findings

Achieves superior accuracy over baselines on ERA5 dataset.

Ensures physical plausibility in reconstructed atmospheric states.

Enhances data assimilation with physics-informed generative modeling.

Abstract

Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models have shown great potential for DA tasks, most existing approaches remain purely data-driven and often overlook the physical laws that govern complex atmospheric dynamics. As a result, they may yield physically inconsistent reconstructions that impair downstream applications. To overcome this limitation, we propose PhyDA, a physics-guided diffusion framework designed to ensure physical coherence in atmospheric data assimilation. PhyDA introduces two key components: (1) a Physically Regularized Diffusion Objective that integrates physical constraints into the training process by penalizing deviations from known physical laws expressed as partial differential equations, and (2) a Virtual Reconstruction Encoder that bridges observational sparsity for structured latent representations, further enhancing the model's ability to infer complete and physically coherent states. Experiments on the ERA5 reanalysis dataset demonstrate that PhyDA achieves superior accuracy and better physical plausibility compared to state-of-the-art baselines. Our results emphasize the importance of combining generative modeling with domain-specific physical knowledge and show that PhyDA offers a promising direction for improving real-world data assimilation systems.