Uncertainty Quantification for Physics-Informed Traffic Graph Networks

Predicting spatiotemporal patterns is essential for traffic flow forecasting in Intelligent Transportation Systems (ITS), where accurate predictions can greatly enhance traffic management. Currently, data-driven approaches, such as Graph Neural Networks (GNNs) combined with physics-informed partial differential equations (PDEs), have shown promising performance in capturing complex traffic dynamics. However, these models sometimes make unexpected and incorrect predictions with high certainty which will mislead real-world decision-making, particularly in critical scenarios. This lack of uncertainty quantification (UQ), which estimates the confidence of neural network predictions beyond prediction accuracy, limits the reliability of the predictions. Existing UQ methods in traffic forecasting are typically applied to purely data-driven models, leaving the effects of physics-informed approaches on UQ largely unexplored. In this paper, we address these challenges by combining multiple UQ baselines with physics-informed methods to investigate the impact of physical constraints on UQ for traffic forecasting. Additionally, we introduce a new physics-informed loss function to guide the model learning process, which holds an exponential relation and complements the linear relations of the PDE layer. Through extensive experiments on real-world traffic datasets, we demonstrate that our proposed method outperforms existing approaches, achieving reductions of up to 14.8% in short-term and 8.7% in long-term traffic speed prediction errors. Sensitivity analysis further illustrates the robustness of our approach under perturbations.