  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.
