Long-Range Spatio-Temporal Graph Propagation Through Oscillations

Graph Neural Networks (GNNs) are powerful tools for learning from spatio-temporal data, as interactions in space can be naturally described by a graph structure. However, capturing long-range dependencies becomes substantially harder when information must flow through space and time simultaneously. Most existing approaches extend GNNs from static graphs to temporal settings by alternating propagation between time and space. In this work, we introduce STORM, a differential-equation-inspired GNN that exploits oscillatory dynamics to propagate information effectively in the joint spatio-temporal domain. By combining a wave-equation update with dissipative and external forcing terms, STORM balances conservative and non-conservative dynamics. We provide a bottom-up analysis of the model, highlighting its propagation behavior and stability, and show that STORM is universal. We empirically validate our method on diverse benchmarks, including tasks designed for analyzing long-range spatio-temporal dependencies, real-world forecasting, and a new long-range task inspired by physical simulations. Across these settings, STORM consistently matches or outperforms strong baselines, establishing a new state of the art for long-range spatio-temporal graph learning.