Dynamic Graph Learning-Neural Network for Multivariate Time Series Modeling

Multivariate time series forecasting is a challenging task because the data involves a mixture of long- and short-term patterns, with dynamic spatio-temporal dependencies among variables. Existing graph neural networks (GNN) typically model multivariate relationships with a pre-defined spatial graph or learned fixed adjacency graph. It limits the application of GNN and fails to handle the above challenges. In this paper, we propose a novel framework, namely static- and dynamic-graph learning-neural network (SDGL). The model acquires static and dynamic graph matrices from data to model long- and short-term patterns respectively. Static matric is developed to capture the fixed long-term association pattern via node embeddings, and we leverage graph regularity for controlling the quality of the learned static graph. To capture dynamic dependencies among variables, we propose dynamic graphs learning method to generate time-varying matrices based on changing node features and static node embeddings. And in the method, we integrate the learned static graph information as inductive bias to construct dynamic graphs and local spatio-temporal patterns better. Extensive experiments are conducted on two traffic datasets with extra structural information and four time series datasets, which show that our approach achieves state-of-the-art performance on almost all datasets. If the paper is accepted, I will open the source code on github.