Incorporating Nonlocal Traffic Flow Model in Physics-Informed Neural Networks

This research contributes to the advancement of traffic state estimation and prediction methodologies by leveraging the benefits of the nonlocal LWR model within a physics-informed deep learning (PIDL) framework. The classical LWR model, while useful, falls short of accurately representing real-world traffic flows due to the assumption that traffic speed is solely dependent upon local traffic density. The nonlocal LWR model addresses this limitation by considering the speed as a weighted mean of the downstream traffic densities. In this paper, we propose a novel PIDL framework that incorporates the nonlocal LWR model paired with Greenshields and Underwood fundamental diagrams. We introduce both fixed-length and variable-length look-ahead kernels for nonlocal speed-density relationships and develop the required mathematics. The proposed PIDL framework undergoes a comprehensive evaluation, assessing various convolutional kernels and look-ahead windows using NGSIM and CitySim datasets. The results demonstrate improvements over the baseline PIDL approach using the local LWR model. The findings highlight the potential of the proposed approach to enhance the accuracy and reliability of traffic state estimation, enabling more effective traffic management strategies.