WaveGSSM: Graph Wave State Space Models for Propagating Spatio-Temporal Patterns

2026-10-05

AI Summary

This study addresses the limitation of spatiotemporal graph models in explicitly representing the dynamic propagation of patterns by proposing a second-order graph state space model. Methodologically, it achieves unified spatiotemporal modeling by coupling the current state with its rate of change, and introduces a "graph wave" transformation mechanism to explicitly characterize inter-node motion dynamics, thereby transcending the conventional decoupled paradigm that processes spatial and temporal dimensions sequentially. Experimental results demonstrate that the proposed model achieves state-of-the-art performance across multiple benchmarks, reducing the RMSE in weather forecasting by an average of 20.2% and significantly enhancing pattern preservation capabilities in large-scale scenarios.

Abstract

Spatio-temporal graph models typically encode each snapshot with a GNN and then connect the resulting representations through a temporal module. This space-then-time design is effective, yet it does not explicitly represent how a pattern moves across the graph. We show empirically that, for a propagating process, the same present field can lead to different futures when its recent rate of change differs, motivating an explicit representation of motion in the predictive state. We introduce WaveGSSM, a second-order graph state-space model that maintains two coupled latent states at each node, one for the current pattern and one for its temporal rate of change. A graph-wave transition updates the motion state through graph interactions and uses it to advance the pattern state, coupling spatial propagation and temporal evolution within a single rollout. We evaluate WaveGSSM on four temporal-graph benchmarks and global weather forecasting. It consistently achieves the best mean performance across the temporal-graph benchmarks and reduces the geopotential RMSE by 20.2% on average for 1- to 5-day weather forecasts relative to a backbone-matched snapshot model, while better preserving large-scale atmospheric patterns.

Problem

• spatio-temporal graph
• propagating patterns
• state space model
• motion representation
• temporal dynamics

Innovation

• Graph State Space Model
• Spatio-Temporal Graph
• Second-Order Dynamics
• Graph-Wave Transition
• Weather Forecasting