Physics-Informed Directed Spatio-Temporal Graph Convolutional Networks for Traffic Flow Prediction

Accurate urban traffic flow prediction is crucial for Intelligent Transportation Systems (ITS). Existing spatio-temporal neural networks typically adopt symmetric adjacency matrices, failing to capture the asymmetric spatial dependencies of traffic flow, and lack macroscopic physical constraints, leading to non-conservative predictions in long-term forecasting. To address these issues, we propose PI-Dir-STGCN. Unlike prior methods that loosely couple physical penalties with graph networks, our framework achieves a tight structural coupling between directed graph structures and macroscopic traffic dynamics. Specifically, we construct an asymmetric directed weighted adjacency matrix to capture these asymmetric traffic dependencies, and develop a graph-topology generalized upwind difference scheme to embed the LWR model into the graph neural network. This innovation transforms the directed graph into a numerical grid for fluid dynamics and encourages mass-conserving predictions through a computable physics residual. Experiments on PeMS04 and PeMS08 show that our model effectively suppresses cumulative errors, integrates data-driven learning with physical evolution, and provides strong physical interpretability.