Online Traffic Density Estimation using Physics-Informed Neural Networks

TL;DR

This paper introduces 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.

Abstract

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.

Figures (8)

• Figure 1: The black lines are the paths $x_i$ of the probe vehicles $i$, in which sensor data $\rho(\cdot, x_i(\cdot))$ is measured.
• Figure 2: The PINN for traffic density reconstruction.
• Figure 3: Framework for using a PINN for online real-time estimation using iterative learning.
• Figure 4: The time scale for training a new PINN iteration at time $i\delta_t$.
• Figure 5: Reconstructed and simulated data, in the case of varying free flow velocity, leading to areas of imperfect model knowledge.