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

2025-05-08

AI Summary

Existing deep learning weather forecasting models often neglect atmospheric physical principles and Earth’s spherical topology, limiting prediction accuracy. To address this, we propose the first end-to-end framework that jointly integrates spherical differential equation solvers—modeling advection and the Navier–Stokes equations—with spherical graph neural networks (Spherical GNNs), explicitly encoding Earth’s curvature, conservation laws, and atmosphere–land coupling mechanisms. Our approach leverages a spherical numerical solver coupled with multi-physics joint modeling, trained and evaluated on ERA5 data at 5.625° resolution. Experiments demonstrate that our method significantly outperforms state-of-the-art deep learning baselines and the operational ECMWF Integrated Forecasting System (IFS) at T42 resolution across medium- to short-term forecasting tasks. This work establishes a novel paradigm for physics-informed spherical spatiotemporal modeling, bridging geometric deep learning with fundamental geophysical dynamics.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the extbf{physics} of the underlying weather evolution or the extbf{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.

Problem

• Incorporates physics and topology in weather prediction models
• Addresses Earth-atmosphere interaction modeling challenges
• Improves accuracy over existing deep learning and numerical methods

Innovation

• Physics-assisted deep learning for weather prediction
• Topology-informed spherical graph neural network
• Numerical solving on spherical manifold