Learning "Look-Ahead" Nonlocal Traffic Dynamics in a Ring Road

The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR) traffic model, nonlocal partial differential equation (PDE) models with ``look-ahead" dynamics have been proposed, which assume that the speed is a function of weighted downstream traffic density. However, it lacks data validation on two important questions: whether there exist nonlocal dynamics, and how the length and weight of the ``look-ahead" window affect the spatial temporal propagation of traffic densities. In this paper, we adopt traffic trajectory data from a ring-road experiment and design a physics-informed neural network to learn the fundamental diagram and look-ahead kernel that best fit the data, and reinvent a data-enhanced nonlocal LWR model via minimizing the loss function combining the data discrepancy and the nonlocal model discrepancy. Results show that the learned nonlocal LWR yields a more accurate prediction of traffic wave propagation in three different scenarios: stop-and-go oscillations, congested, and free traffic. We first demonstrate the existence of ``look-ahead" effect with real traffic data. The optimal nonlocal kernel is found out to take a length of around 35 to 50 meters, and the kernel weight within 5 meters accounts for the majority of the nonlocal effect. Our results also underscore the importance of choosing a priori physics in machine learning models.