Spatial-Temporal PDE Networks for Traffic Flow Forecasting

Spatial-temporal forecasting is crucial in various domains, including traffic flow prediction for Intelligent Transportation Systems (ITS). Despite the challenges posed by complex spatial-temporal dependencies in traffic networks, Partial Differential Equations (PDEs) have proven effective for capturing traffic dynamics. However, recent trends favor data-driven approaches like Graph Neural Networks (GNNs) for traffic forecasting, often overlooking the principles described by PDEs. In this paper, we propose a Graph Partial Differential Equation Network (GPDE) that integrates PDE principles with GNNs to enhance traffic flow forecasting. Our approach leverages dynamic graph structures based on PDE flux functions, incorporating residual connections and learnable rates for improved model performance. Extensive experiments on real-world traffic datasets demonstrate the superiority of GPDE over existing methods in both short-term and long-term traffic speed prediction tasks.