A Physics Informed GNN for Traffic Prediction: the DeepCTM Model

This paper proposes DeepCTM, a physics-constrained neural architecture designed to connect the fields of graph representation learning and the fundamental kinematic laws of traffic flow on road networks. Accurate traffic flow forecasting is a critical component for correctly preventing traffic jams and managing road interventions: deep learning models often produce physically inconsistent predictions (e.g., violating mass conservation), especially when stationary sensor coverage along the infrastructure is sparse or incomplete. To address this limitation, DeepCTM transforms the neural network into a physics-aware simulator. The architecture is based on the Physics-Augmented LSTM (PA-LSTM), which partitions the internal memory into a physical subspace, anchored to the Cell Transmission Model (CTM), and a free subspace dedicated to capturing stochastic human anomalies. To maintain topological continuity, the road network is discretized to include both observed sensor nodes (Vobs) and virtual nodes (Vvirt), allowing the model to propagate physical constraints even through unmonitored areas via an adaptive gating mechanism. Experimental evaluations conducted on the Madrid urban network dataset demonstrate an encouraging performance of DeepCTM over state of the art baselines. By enforcing physical consistency through a spatiotemporal multi-objective loss, the model reaches comparable results compared to modern GNN and statistical methods but, most notably, DeepCTM exhibits robustness in spatial inference, accurately reconstructing traffic dynamics.