State Feedback Enhanced Graph Differential Equations for Multivariate Time Series Forecasting

Abstract

Multivariate time series forecasting holds significant theoretical and practical importance in various fields, including web analytics and transportation. Recently, graph neural networks and graph differential equations have shown exceptional capabilities in modeling spatio-temporal features. However, existing methods often suffer from over-smoothing, hindering real-world problem-solving. In this work, we analyze the graph propagation process as a dynamical system and propose a novel feedback mechanism to enhance representation power, adaptively adjusting the representations to align with desired performance outcomes, thereby fundamentally mitigating the issue of over-smoothing. Moreover, we introduce an effective multivariate time series forecasting model called SF-GDE, based on the proposed graph propagation with the feedback mechanism. Intensive experiments are conducted on three real-world datasets from diverse fields. Results show that SF-GDE outperforms the state of the arts, and the feedback mechanism can serve as a universal booster to improve performance for graph propagation models.