Frequency as identity: A Fourier hypernetwork for spatiotemporal forecasting

Long-term sequence forecasting (LSTF) and spatiotemporal forecasting (STF) are two classic instances of multivariate time series prediction. While Fourier transform-based frequency domain modeling paradigms have gained significant attention and been successfully applied to LSTF tasks in recent years, their effectiveness diminishes in spatiotemporal prediction scenarios involving extensive sensor networks. This is because multiple sensors exhibit more pronounced frequency characteristic variations across different time steps compared to systems with fewer sensors, invalidating the assumption of stable frequency characteristics across all sensor signals that underlie Fourier-based time series modeling. Consequently, Graph Neural Networks (GNNs) have emerged as the mainstream approach for spatiotemporal sequence modeling.In this paper, we propose S patio- T emporal P attern I dentity A ttachment ( STPIA ), a novel Fourier modeling paradigm for STF. Instead of directly using Fourier transform auxiliary variables for prediction, we design a hypernetwork that receives frequency domain information post-Fourier transformation. Through carefully designed differential sampling strategies, the frequency domain identity information of each node is attached to node embeddings. We further combine this pattern information with dynamic embeddings to extract richer spatiotemporal features, employing a two-layer Transformer as STPIA’s backbone network. We demonstrate that the embeddings generated by the hyper network in the frequency domain benefit from energy compaction and can better identify node patterns and distinguish between nodes, which addresses the fundamental challenge of STF. Experiments on six datasets show STPIA’s superior performance over all baseline models with an average improvement of approximately 3.44 %. We provide an interpretability analysis of the advantages of frequency domain modeling, demonstrating its enhanced node differentiation capabilities. Additionally, we explore the underlying principles of frequency domain modeling advantages from an energy perspective, offering guidance for future frequency domain spatiotemporal models. • Proposes STPIA, a Fourier-hypernetwork model that learns unique node identities. • Achieves SOTA performance by effectively differentiating nodes via frequency patterns. • Demonstrates robustness to non-stationarity with an energy-based model interpretation.