Physics-Informed Bidirectional Graph Networks for Traffic Prediction: Deriving Message Passing Direction from Traffic Flow Theory

Benjamin Lartey

Keywords: Traffic Prediction, Graph Networks, Physics Informed Networks, Traffic Flow Theory

Abstract: Traffic prediction is essential for intelligent transportation systems, yet existing graph neural networks treat spatial message passing as direction-agnostic, ignoring the physics of traffic wave propagation. We propose RA-BiGN, a physics-informed bidirectional graph network that derives its message passing direction from the Lighthill-Whitham-Richards (LWR) traffic flow model. Our key insight is that the characteristic speed $c = v_f(1 - 2\rho/\rho_{\max})$ determines whether information propagates downstream (free-flow, $c > 0$) or upstream (congestion/shockwaves, $c < 0$). We embed this physics into a learnable propagation weight $\alpha$ that dynamically balances bidirectional graph convolution based on local traffic state. Experiments on PEMS04 and PEMS08 demonstrate competitive performance with state-of-the-art methods, while ablations confirm that physics-informed $\alpha$ outperforms uniform weighting. Crucially, visualizations show the learned $\alpha$ correlates with speed and occupancy exactly as LWR theory predicts, validating our physics-grounded design. Our work suggests that incorporating domain-specific physical laws into GNN architectures is a promising direction for spatiotemporal forecasting.

Submission Number: 2