Second Order Physics-Informed Learning of Road Density using Probe Vehicles

TL;DR

This paper introduces a physics-informed learning method using a second-order traffic model to accurately reconstruct traffic density from sparse vehicle trajectory data, especially in dynamic conditions.

Contribution

It combines a second-order Aw-Rascle and Zhang model with a first-order stage to improve traffic density reconstruction from limited data.

Findings

Second-order model yields more accurate reconstructions in transient traffic regimes.

Learning equilibrium velocity improves steady-state reconstruction but can cause instability in transient regimes.

Second-order approach outperforms first-order methods in nonequilibrium conditions.

Abstract

We propose a Physics Informed Learning framework for reconstructing traffic density from sparse trajectory data. The approach combines a second-order Aw-Rascle and Zhang model with a first-order training stage to estimate the equilibrium velocity. The method is evaluated in both equilibrium and transient traffic regimes using SUMO simulations. Results show that while learning the equilibrium velocity improves reconstruction under steady state conditions, it becomes unstable in transient regimes due to the breakdown of the equilibrium assumption. In contrast, the second-order model consistently provides more accurate and robust reconstructions than first-order approaches, particularly in nonequilibrium conditions.