Physics-Assisted and Topology-Informed Deep Learning for Weather Prediction

TL;DR

PASSAT is a physics-assisted, topology-aware deep learning model that improves weather prediction by integrating physical laws and Earth's surface topology, outperforming existing models on ERA5 data.

Contribution

The paper introduces PASSAT, a novel deep learning model that incorporates physical equations and Earth's topology for enhanced weather prediction accuracy.

Findings

PASSAT outperforms state-of-the-art deep learning models.

PASSAT surpasses operational numerical weather prediction models.

The model effectively integrates physical laws and topology.

Abstract

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.