Learning Time-aware Graph Structures for Spatially Correlated Time Series Forecasting

Abstract

Spatio-temporal forecasting of future values of spatially correlated time series is important across many cyber-physical systems (CPS). Recent studies offer evidence that the use of graph neural networks to capture latent correlations between time series holds a potential for enhanced forecasting. However, most existing methods rely on pre-defined or self-learning graphs, which are either static or unintentionally dynamic, and thus cannot model the time-varying correlations that exhibit trends and periodicities caused by the regularity of the underlying processes in CPS. To tackle such limitation, we propose Time-aware Graph Structure Learning (TagSL), which extracts time-aware correlations among time series by measuring the interaction of node and time representations in high-dimensional spaces. Notably, we introduce time discrepancy learning that utilizes contrastive learning with distance-based regularization terms to constrain learned spatial correlations to a trend sequence. Additionally, we propose a periodic discriminant function to enable the capture of periodic changes from the state of nodes. Next, we present a Graph Convolution-based Gated Recurrent Unit (GCGRU) that jointly captures spatial and temporal dependencies while learning time-aware and node-specific patterns. Finally, we introduce a unified framework named Time-aware Graph Convolutional Recurrent Network (TGCRN), combining TagSL, and GCGRU in an encoder-decoder architecture for multi-step spatio-temporal forecasting. We report on experiments with TGCRN and popular existing approaches on five real-world datasets, thus providing evidence that TGCRN is capable of advancing the state-of-the-art. We also cover a detailed ablation study and visualization analysis, offering detailed insight into the effectiveness of time-aware structure learning.