# Learning-based Traffic State Reconstruction using Probe Vehicles

arXiv: https://arxiv.org/abs/2011.05031 · HTML: https://mlsanity.com/paper/2011.05031/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 10 of 10)

- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Applications of deep learning in traffic congestion detection, prediction and alleviation: A survey](https://mlsanity.com/paper/2102.09759/) (2021)
- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimation](https://mlsanity.com/paper/2102.02906/) (2021)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Short-term traffic prediction using physics-aware neural networks](https://mlsanity.com/paper/2109.10253/) (2021)
- [Learning Traffic Speed Dynamics from Visualizations](https://mlsanity.com/paper/2105.01423/) (2021)
- [ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors](https://mlsanity.com/paper/2503.14053/) (2025)
- [PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observations](https://mlsanity.com/paper/2512.06183/) (2025)
- [Estimating Traffic Speeds using Probe Data: A Deep Neural Network Approach](https://mlsanity.com/paper/2104.09686/) (2021)

## Abstract (arXiv)

This article investigates the use of a model-based neural-network for the traffic reconstruction problem using noisy measurements coming from probe vehicles. The traffic state is assumed to be the density only, modeled by a partial differential equation. There exist various methods for reconstructing the density in that case. However, none of them perform well with noise and very few deal with lagrangian measurements. This paper introduces a method that can reduce the processes of identification, reconstruction, prediction, and noise rejection into a single optimization problem. Numerical simulations, based either on a macroscopic or a microscopic model, show good performance for a moderate computational burden.