# Incorporating Nonlocal Traffic Flow Model in Physics-informed Neural Networks

arXiv: https://arxiv.org/abs/2308.11818 · HTML: https://mlsanity.com/paper/2308.11818/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 5 of 5)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [CitySim: A Drone-Based Vehicle Trajectory Dataset for Safety Oriented Research and Digital Twins](https://mlsanity.com/paper/2208.11036/) (2022)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [On the Limitations of Physics-informed Deep Learning: Illustrations Using First Order Hyperbolic Conservation Law-based Traffic Flow Models](https://mlsanity.com/paper/2302.12337/) (2023)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)

## Abstract (arXiv)

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.