Evolving graph structure learning for multivariate time series forecasting

In recent years, the application of graph neural networks (GNN) in multivariate time series forecasting has yielded remarkable achievements. The adjacency matrix which describes the interactions among variables is dense and static in most previous efforts no matter hand-crafted or self-learned. However, we argue that: (1) In the real-world scenario, the interactions could be dynamic and evolving; (2) A sparse and compact graph structure could better reflect such interactions. Along this line, this paper proposes a deep neural network based on GNN to address multivariate time series forecasting problem. Firstly, we construct a sparse and principal structure from the original dense graph structure differentiably by Gumbel-Softmax. Secondly, a new series of graphs are constructed by the recurrent neural network to model the evolving correlations among variables during each individual time point. Thirdly, a novel temporal constraint which is aimed at enhancing the training process is proposed to help evolving graphs capture the temporal smoothness of time series. Lastly, a unified neural network is constructed that integrates all of the above modules to make the final prediction, effectively addressing both temporal dependency and pairwise correlations in a comprehensive manner. Experiments are performed on six datasets comprising various domains, evaluating the performance of our model in single-step and multi-step forecasting tasks. The results showcase the exceptional performance of our model compared to the existing approaches in the field.