Second Order Physics-Informed Learning of Road Density using Probe Vehicles
This work addresses traffic density estimation for urban planning and management, but it is incremental as it builds on existing physics-informed learning methods.
The paper tackled reconstructing traffic density from sparse trajectory data by proposing a Physics Informed Learning framework that combines a second-order Aw-Rascle and Zhang model with a first-order training stage. Results showed that the second-order model provided more accurate and robust reconstructions than first-order approaches, particularly in nonequilibrium conditions, though learning the equilibrium velocity improved steady-state performance but became unstable in transient regimes.
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.