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

TL;DR

PASSAT addresses the gap between physics-based weather modeling and data-driven approaches by integrating the advection equation and the Navier–Stokes dynamics on a spherical manifold with a topology-aware spherical graph neural network to capture Earth–atmosphere interactions. It jointly learns initial velocity fields and atmospheric tendencies from historical data, and performs autoregressive predictions with a stable time integration scheme, all while operating on the sphere to avoid planar distortions. Evaluated on $5.625^\circ$ ERA5 data, PASSAT outperforms state-of-the-art DL baselines and the operational IFS $T42$ model, with GraphCast being the closest competitor that lacks explicit physics constraints. The results demonstrate the value of combining physics-informed priors with topology-aware learning for robust, medium-term global weather prediction, and point toward extensions to more variables, higher resolution, and more efficient integrators.

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.

Figures (11)

• Figure 1: Attributions of the weather evolution.
• Figure 2: Distortions due to planar projection. (a) The spherical and planner representations of the global weather. (b) The same weather patterns on the sphere are distorted on the plane. (c) The convolutions on the sphere are distorted on the plane.
• Figure 3: Overview of PASSAT.
• Figure 4: Overview of PASSAT's graph neural network. TOP: The backbone model and two branches. BOTTOM: The basic block.
• Figure 5: Comparison between PASSAT and other models. The x-axis represents the lead time in hours. Smaller RMSE and larger ACC values indicate better performance. Note that some results of IFS T42 exceed the bounds.