Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the \textbf{physics} of the underlying weather evolution or the \textbf{topology} of the Earth's surface. In light of these disadvantages, we develop PASSAT, a novel Physics-ASSisted And Topology-informed deep learning model for weather prediction. PASSAT attributes the weather evolution to two key factors: (i) the advection process that can be characterized by the advection equation and the Navier-Stokes equation; (ii) the Earth-atmosphere interaction that is difficult to both model and calculate. PASSAT also takes the topology of the Earth's surface into consideration, other than simply treating it as a plane. With these considerations, PASSAT numerically solves the advection equation and the Navier-Stokes equation on the spherical manifold, utilizes a spherical graph neural network to capture the Earth-atmosphere interaction, and generates the initial velocity fields that are critical to solving the advection equation from the same spherical graph neural network. In the $5.625^\circ$-resolution ERA5 data set, PASSAT outperforms both the state-of-the-art deep learning-based weather prediction models and the operational numerical weather prediction model IFS T42. Code and checkpoint are available at https://github.com/Yumenomae/PASSAT_5p625.

本研究针对现有天气预测深度学习模型忽略天气演变物理及地球表面拓扑结构的问题，提出了一种新的模型PASSAT。PASSAT通过考虑大气对流过程和地球-大气相互作用，结合球面图神经网络，显著提升预测精度，超越了当前最先进的天气预测模型和数值天气预报模型。

基于物理辅助和拓扑信息的深度学习天气预测