Incorporating Nonlocal Traffic Flow Model in Physics-informed Neural
  Networks
Archie J. Huang Animesh Biswas Shaurya Agarwal
This research contributes to the advancement of traffic state estimation
methods by leveraging the benefits of the nonlocal LWR model within a
physics-informed deep learning framework. The classical LWR model, while
useful, falls short of accurately representing real-world traffic flows. The
nonlocal LWR model addresses this limitation by considering the speed as a
weighted mean of the downstream traffic density. In this paper, we propose a
novel PIDL framework that incorporates the nonlocal LWR model. We introduce
both fixed-length and variable-length kernels and develop the required
mathematics. The proposed PIDL framework undergoes a comprehensive evaluation,
including various convolutional kernels and look-ahead windows, using data from
the 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.