Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting

TL;DR

PhyDL-NWP tackles the mismatch between traditional NWP and DL by embedding physics into a continuous-weather predictor. It models weather fields with a surrogate $f_\theta(x,y,t)$ and learns a parameterized PDE $\frac{\partial u}{\partial t}=Q_\pi(x,y,t)+\Phi(u)\Xi$, including a latent force $Q_\pi$ to represent unresolved physics, enabling resolution-free downscaling and physically consistent forecasting. The framework supports fine-tuning pre-trained forecasting models via a physics-guided loss, using finite differences for efficient derivatives, and demonstrates substantial improvements in both downscaling and forecasting across regional and global datasets, while achieving up to 170x faster inference with ~55K parameters. The learned dynamics align with established meteorological PDEs, providing interpretable insights into the governing processes and enabling robust, scalable deployment in operational contexts.

Abstract

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

Figures (5)

• Figure 1: Schematic diagram of PhyDL-NWP for downscaling. First, given a continuous input coordinate $(x,y,t)$, the surrogate model $f_\theta$ approximates the weather data. Then, based on PyTorch's auto-differentiation and the existing meteorology theory, we calculate the derivatives for the construction of physical mechanisms driven by PDE. Last, based on linear regression, we learn the PDE that fits the weather data well to provide physical guidance.
• Figure 2: Schematic diagram of PhyDL-NWP for forecasting. We first use pre-trained surrogate model for weather downscaling to perform data augmentation, which is a necessity for aligning weather data resolution in the forecasting model. Then, we take the augmented historical data and use a pre-trained state-of-the-art forecasting model to predict future data. Based on the spatio-temporal coordinates of the predicted data, we add a physics loss to recover the previously learned PDE.
• Figure 3: Model comparison in Ningxia dataset before and after physics guidance for a variety of forecasting ranges on the average of all weather variables.
• Figure 4: Example of comparison of 7-day weather forecast results in Ningxia dataset. AFNO+ are closer to the ground truth.
• Figure 5: The latent force and PDE for the temperature variation in WeatherBench dataset.