# Physics-informed Learning for Identification and State Reconstruction of Traffic Density

arXiv: https://arxiv.org/abs/2103.13852 · HTML: https://mlsanity.com/paper/2103.13852/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2021.

## Built on by (most cited first, 13 of 13)

- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (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)
- [PassionNet: An Innovative Framework for Duplicate and Conflicting Requirements Identification](https://mlsanity.com/paper/2412.01657/) (2024)
- [Inverting the Fundamental Diagram and Forecasting Boundary Conditions: How Machine Learning Can Improve Macroscopic Models for Traffic Flow](https://mlsanity.com/paper/2303.12740/) (2023)
- [Physics-informed Neural Network Combined with Characteristic-Based Split for Solving Navier-Stokes Equations](https://mlsanity.com/paper/2304.10717/) (2023)
- [MILP initialization for solving parabolic PDEs with PINNs](https://mlsanity.com/paper/2501.16153/) (2025)
- [ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors](https://mlsanity.com/paper/2503.14053/) (2025)
- [Online Traffic Density Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2504.03483/) (2025)
- [(Un)supervised Learning of Maximal Lyapunov Functions](https://mlsanity.com/paper/2408.17246/) (2024)
- [Closed-Loop Neural Operator-Based Observer of Traffic Density](https://mlsanity.com/paper/2504.04873/) (2025)
- [Traffic Flow Reconstruction from Limited Collected Data](https://mlsanity.com/paper/2602.11336/) (2026)

## Abstract (arXiv)

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model used assumes noisy measurements and a partially unknown first-order model. All these considerations make the use of machine learning to reconstruct the state the only applicable solution. We first investigate how the identification and reconstruction processes can be merged and how a sparse dataset can still enable a good identification. Secondly, we propose a pre-training procedure that aids the hyperparameter tuning, preventing the gradient descent algorithm from getting stuck at saddle points. Examples using numerical simulations and the SUMO traffic simulator show that the reconstructions are close to the real density in all cases.