Learning to Learn the Macroscopic Fundamental Diagram using Physics-Informed and meta Machine Learning techniques

Abstract: The Macroscopic Fundamental Diagram 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 article proposes a framework harnessing meta-learning, a subcategory of machine learning that trains models to understand and adapt to new tasks on their own, to alleviate the data scarcity challenge. The developed model is trained and tested by leveraging data from multiple cities and exploiting it to model the MFD of other cities with different shares of detectors and topological structures. The proposed meta-learning framework is applied to an ad-hoc Multi-Task Physics-Informed Neural Network, specifically designed to estimate the MFD. Results show an average MSE improvement in flow prediction ranging between ~ 17500 and 36000 (depending on the subset of loop detectors tested). The meta-learning framework thus successfully generalizes across diverse urban settings and improves performance on cities with limited data, demonstrating the potential of using meta-learning when a limited number of detectors is available. Finally, the proposed framework is validated against traditional transfer learning approaches and tested with FitFun, a non-parametric model from the literature, to prove its transferability.