Learning to Learn the Macroscopic Fundamental Diagram using physic informed and meta Machine Learning techniques

Abstract

The Macroscopic Fundamental Diagram (MFD) is a popular tool used to describe traffic dynamics in an aggregated way, with applications ranging from traffic control to incident analysis. However, estimating the MFD for a given network requires large numbers of loop detectors, which is not always available in practice. This research proposes using Meta-Learning to alleviate this problem. Specifically, we propose using data from multiple different cities to train a Machine Learning (ML) model that can more accurately learn the MFD using limited data. First, we compare the traditional bi-parabolic model from the literature with a non-parametric Multi-Task Physics-Informed Neural Network (MTPINN). Then, a Model-Agnostic Meta-Learning (MAML) framework is implemented to estimate MFDs when limited data is available. Results show that MAML successfully generalizes across diverse urban settings and improves performance on cities with limited data, and demonstrate the potential of using Meta-Learning when a limited number of detectors is available.