Physics-informed Learning for Identification and State Reconstruction of Traffic Density

TL;DR

This paper introduces a physics-informed machine learning approach for reconstructing traffic density from limited probe vehicle data, effectively handling noisy measurements and partial models.

Contribution

It proposes a unified identification and reconstruction method with a pre-training procedure to improve hyperparameter tuning in traffic density estimation.

Findings

Reconstruction accuracy close to real density in simulations

Effective handling of noisy and sparse data

Pre-training improves hyperparameter tuning

Abstract

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model used assumes noisy measurements and a partially unknown first-order model. All these considerations make the use of machine learning to reconstruct the state the only applicable solution. We first investigate how the identification and reconstruction processes can be merged and how a sparse dataset can still enable a good identification. Secondly, we propose a pre-training procedure that aids the hyperparameter tuning, preventing the gradient descent algorithm from getting stuck at saddle points. Examples using numerical simulations and the SUMO traffic simulator show that the reconstructions are close to the real density in all cases.