Uncertainty Quantification for Physics-Informed Traffic Graph Networks with Adversarial Attacks

Abstract

Predicting spatiotemporal patterns is critical for traffic flow forecasting in Intelligent Transportation Systems (ITS), as accurate predictions can significantly enhance traffic management and decision-making. Recent data-driven approaches, particularly Graph Neural Networks (GNNs) integrated with physics-informed partial differential equations (PDEs), have demonstrated strong capability in modeling complex traffic dynamics. However, these models may still produce overconfident yet incorrect predictions, which can be particularly problematic in safety-critical scenarios. Uncertainty quantification (UQ) enhances the reliability of predictions and the practical application of NNs by estimating prediction confidence, not just accuracy. Despite its importance, existing UQ methods in traffic forecasting are primarily developed for purely data-driven models, and the role of physics-informed modeling in uncertainty estimation remains insufficiently understood. In this paper, we bridge this gap by integrating multiple UQ baseline methods with physics-informed modeling to systematically investigate how physical constraints influence uncertainty estimation in traffic forecasting. We further propose a physics-informed loss function that enhances the model's ability to capture physically consistent dynamics and improves the calibration and reliability of uncertainty estimates. In addition, we evaluate robustness under both noisy and adversarial perturbations, showing that our approach yields more stable predictions and uncertainty estimates under distribution shifts. Extensive experiments on real-world traffic datasets demonstrate that our approach improves both prediction accuracy and uncertainty quality, achieving up to 14.8% improvement in short-term and 8.7% in long-term traffic speed prediction errors, while providing better-calibrated and more robust uncertainty estimates.