Physics-Informed Diffusion Model and Sampling for Global Weather Forecasting

Recent advancements in weather forecasting have shown that generative probabilistic models, particularly diffusion models, exhibit significant promise in spatiotemporal forecasting. These models demonstrate enhanced accuracy, surpassing both machine learning-based deterministic models and traditional Numerical Weather Prediction (NWP) models, especially in short-range forecasting. However, a key challenge in utilising diffusion models for long lead time predictions is the increased variance in samples, which complicates the identification of the most accurate predictions. Specifically, ensemble means from samples at longer lead times often lack the necessary granularity to provide detailed and accurate predictions. This study addresses these challenges by introducing a novel approach: a physics-informed diffusion model coupled with physics-based sampling strategies. We incorporate physical information into the diffusion model as guiding constraints, and apply additional knowledge-based control to reduce the diversity in predictions, aiming for more consistent and reliable forecasts. The effectiveness of various types of physical information and the methods used to integrate this physics into the diffusion model are evaluated on WeatherBench2. Furthermore, we propose a unique physics-based sampling technique that utilises conservation laws. This methodology is designed to enable the selection of predictions that are most consistent with physical principles, potentially enhancing the model's capability in accurately forecasting extreme weather events. By integrating physical laws and principles into both the diffusion model and the sampling process, this approach aims to improve the overall accuracy and reliability of long-range weather predictions. The combination of physics-informed modelling and physics-based sampling offers a new strategy in generative model for weather forecasting.