Physics-Informed Bayesian Deep Learning for Traffic State Estimation and Uncertainty Quantification

Traffic state estimation (TSE) is a crucial component for efficient traffic control and management. In the literature, given limited and potentially noisy traffic observations, a variety of model-driven and data-driven TSE approaches are developed to reconstruct traffic state variables, such as vehicle density and velocity. In practice, the confidence levels of the reconstruction output also carry valuable insights for transportation practitioners and engineers to develop traffic control measures. In this work, we propose the adoption of the physics-informed Bayesian deep learning (PIBDL) neural network for traffic state estimation and uncertainty quantification (TSE-UQ). Equipped with the knowledge of flow conservation laws, the physics-informed neural network has the advantage of accurately estimating the traffic states, and the component of Bayesian inference in PIBDL enables UQ of the TSE output. We demonstrate the effectiveness of the proposed approach by designing a case study with a synthetic vehicle density dataset, and comparing the PIBDL performance to a baseline deep learning (DL) neural network in TSE-UQ. The results from the case study demonstrate the capability of PIBDL in TSE-UQ applications.