Online Traffic Density Estimation using Physics-Informed Neural Networks

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.

@article{wilkman2025_2504.03483,
  title={ Online Traffic Density Estimation using Physics-Informed Neural Networks },
  author={ Dennis Wilkman and Kateryna Morozovska and Karl Henrik Johansson and Matthieu Barreau },
  journal={arXiv preprint arXiv:2504.03483},
  year={ 2025 }
}