Learning Time-aware Graph Structures for Spatially Correlated Time
  Series Forecasting
Minbo Ma Jilin Hu Christian S. Jensen Fei Teng Peng Han Zhiqiang Xu Tianrui Li
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.