Traffic Flow Reconstruction between PDEs and Machine Learning

par Nail Baloul

vendredi 10 oct. 2025, 11:00 → 11:30 Europe/Paris

XR203 (XLIM)

We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles, relying solely on the initial and final positions of a small subset of cars. Due to the scarcity of collected data, we generate artificial trajectories using microscopic dynamical systems and design a machine learning model to approximate the traffic density. 

In recent work, researchers have incorporated physics-informed neural networks (PINNs) to enforce conservation laws via PDE-derived Lagrangian terms, which necessitated real-time measurements. In contrast, our method requires less information, leveraging only the initial and final positions of probe vehicles, thus simplifying data collection. 

Our method uses a residual network (ResNet) to analyze traffic dynamics. The learning process is set up as a constrained optimization problem. Starting from observed initial positions, the network predicts future states while incorporating physics-based principles of traffic flow. 

Ultimately, we prove that, when using only synthetic data from dynamical systems, our learned traffic density approximation converges to the LWR macroscopic model as the number of vehicles increases.