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WaveGSSM introduces a novel second-order graph state-space model that explicitly captures the motion of propagating patterns by coupling spatial and temporal evolution within a single rollout. By maintaining latent states for both current patterns and their rates of change, this approach outperforms standard space-then-time designs on benchmarks and significantly improves global weather forecasting accuracy. The method demonstrates how advanced machine learning architectures can better model dynamic physical systems without relying on separate encoding modules.
WaveGSSM: Graph Wave State Space Models for Propagating Spatio-Temporal Patterns
arXiv:2610.06540v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2610.06540 [cs.LG]
(or arXiv:2610.06540v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.06540 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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