CSD: Weather forecasting with graph neural network based on cross-scale diffusivity

Automated weather stations play a pivotal role in fine-grained weather forecasting, due to their cost-effectiveness and global deployment potential. Data-driven methods, particularly deep learning techniques, have emerged as potent tools for precise weather forecasting. However, capturing meaningful relationships among these decentralized stations, especially on global scale, presents a formidable challenge. Many transformer-based approaches, commonly used in data-driven forecasting, rely on the conventional point-wise or the series-wise attention mechanism to construct these relationships between weather stations. Unfortunately, this mechanism either brings about high computational complexity or falls short in explicitly capturing contextual dependencies, as it operates on keys and values derived from the same series of data. In this paper, we propose a novel approach that can adaptively establish cross-scale diffusivity from an energy-constrained diffusion perspective. Additionally, our model can adaptively learn two types of graphs: the static spatial graph and the dynamic temporal graph. Experimental results demonstrate that our method can achieve state-of-the-art performance.