# Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensing

arXiv: https://arxiv.org/abs/2011.09871 · HTML: https://mlsanity.com/paper/2011.09871/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2020.

## Built on by (most cited first, 7 of 7)

- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [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)
- [Generalized adaptive smoothing based neural network architecture for traffic state estimation](https://mlsanity.com/paper/2301.03439/) (2023)
- [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)
- [Traffic Flow Reconstruction from Limited Collected Data](https://mlsanity.com/paper/2602.11336/) (2026)

## Abstract (arXiv)

The state reconstruction problem of a heterogeneous dynamic system under sporadic measurements is considered. This system consists of a conversation flow together with a multi-agent network modeling particles within the flow. We propose a partial-state reconstruction algorithm using physics-informed learning based on local measurements obtained from these agents. Traffic density reconstruction is used as an example to illustrate the results and it is shown that the approach provides an efficient noise rejection.