# Online Traffic Density Estimation using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2504.03483 · HTML: https://mlsanity.com/paper/2504.03483/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 4 Apr 2025.

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

- [Physics-informed Learning for Identification and State Reconstruction of Traffic Density](https://mlsanity.com/paper/2103.13852/) (2021)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensing](https://mlsanity.com/paper/2011.09871/) (2020)
- [Dynamic Traffic Reconstruction using Probe Vehicles](https://mlsanity.com/paper/2007.09914/) (2020)
- [Physics Informed Deep Learning: Applications in Transportation](https://mlsanity.com/paper/2302.12336/) (2023)

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

- [Real-Time Traffic Density Estimation: A Hybrid Computer Vision and Predictive Machine Learning Pipeline](https://mlsanity.com/paper/2610.14326/) (2026)

## Abstract (arXiv)

Recent works on the application of Physics-Informed Neural Networks to traffic density estimation have shown to be promising for future developments due to their robustness to model errors and noisy data. In this paper, we introduce a methodology for online approximation of the traffic density using measurements from probe vehicles in two settings: one using the Greenshield model and the other considering a high-fidelity traffic simulation. The proposed method continuously estimates the real-time traffic density in space and performs model identification with each new set of measurements. The density estimate is updated in almost real-time using gradient descent and adaptive weights. In the case of full model knowledge, the resulting algorithm has similar performance to the classical open-loop one. However, in the case of model mismatch, the iterative solution behaves as a closed-loop observer and outperforms the baseline method. Similarly, in the high-fidelity setting, the proposed algorithm correctly reproduces the traffic characteristics.