B-TSE-PINN: Bayesian-enhanced physics-informed neural networks for uncertainty quantification in traffic states estimation
Date:
Miao, T., Liang, H., & Ye, Y.* (2025, December 8-9). B-TSE-PINN: Bayesian-enhanced physics-informed neural networks for uncertainty quantification in traffic states estimation [Oral Presentation]. The 29th International Conference of Hong Kong Society for Transportation Studies, Hong Kong, China.
Abstract: Traffic state estimation (TSE), a core component of intelligent transportation systems, is challenged by the inherent uncertainty in traffic dynamics and sparse data availability. While deep learning models excel at fitting complex patterns, they often lack physical consistency and fail to provide reliability guarantees. Physics-informed neural networks (PINNs) address the consistency issue but remain deterministic. To overcome these limitations, this paper introduces the B-TSE-PINN, a novel framework that integrates a Bayesian neural network with the physical constraints of the Lighthill-Whitham-Richards (LWR) traffic flow model to perform TSE with Uncertainty Quantification (TSE-UQ). By treating neural network weights as probability distributions, B-TSE-PINN learns a posterior distribution over the solution space, enabling it to decompose predictive uncertainty into its epistemic and aleatoric components. This provides not only an accurate point estimate of traffic states but also a well-calibrated measure of confidence in its predictions. The framework is implemented on an open-source dataset. The results demonstrate that B-TSE-PINN significantly outperforms both purely data-driven and deterministic physics-informed baselines in prediction accuracy. Furthermore, results show that the quantified uncertainties are physically meaningful: epistemic uncertainty correlates with data scarcity and model convergence, while aleatoric uncertainty correlates with traffic congestion levels. B-TSE-PINN offers a robust and trustworthy paradigm for TSE-UQ, paving the way for more reliable and risk-aware decision-making in traffic management.