# Closed-Loop Neural Operator-Based Observer of Traffic Density

arXiv: https://arxiv.org/abs/2504.04873 · HTML: https://mlsanity.com/paper/2504.04873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 7 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Physics-informed Learning for Identification and State Reconstruction of Traffic Density](https://mlsanity.com/paper/2103.13852/) (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)
- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
- [Highway Traffic State Estimation with Mixed Connected and Conventional Vehicles](https://mlsanity.com/paper/1504.06879/) (2015)
- [KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning](https://mlsanity.com/paper/2501.11655/) (2025)
- [Dynamic Traffic Reconstruction using Probe Vehicles](https://mlsanity.com/paper/2007.09914/) (2020)

## Abstract (arXiv)

We consider the problem of traffic density estimation with sparse measurements from stationary roadside sensors. Our approach uses Fourier neural operators to learn macroscopic traffic flow dynamics from high-fidelity data. During inference, the operator functions as an open-loop predictor of traffic evolution. To close the loop, we couple the open-loop operator with a correction operator that combines the predicted density with sparse measurements from the sensors. Simulations with the SUMO software indicate that, compared to open-loop observers, the proposed closed-loop observer exhibits classical closed-loop properties such as robustness to noise and ultimate boundedness of the error. This shows the advantages of combining learned physics with real-time corrections, and opens avenues for accurate, efficient, and interpretable data-driven observers.