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

arXiv: https://arxiv.org/abs/2508.14137 · HTML: https://mlsanity.com/paper/2508.14137/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 67 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [Advances and Challenges in Meta-Learning: A Technical Review](https://mlsanity.com/paper/2307.04722/) (2023)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Cross-city Few-Shot Traffic Forecasting via Traffic Pattern Bank](https://mlsanity.com/paper/2308.09727/) (2023)
- [Meta-QSAR: a large-scale application of meta-learning to drug design and discovery](https://mlsanity.com/paper/1709.03854/) (2017)
- [Urban traffic analysis and forecasting through shared Koopman eigenmodes](https://mlsanity.com/paper/2409.04728/) (2024)
- [STDA-Meta: A Meta-Learning Framework for Few-Shot Traffic Prediction](https://mlsanity.com/paper/2310.20223/) (2023)
- [Deep Learning Methods for Adjusting Global MFD Speed Estimations to Local Link Configurations](https://mlsanity.com/paper/2405.14257/) (2024)

## Built on by (most cited first, 1 of 1)

- [Metalearning traffic assignment for network disruptions with graph convolutional neural networks](https://mlsanity.com/paper/2603.06763/) (2026)

## Abstract (arXiv)

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 practise. This article proposes a framework to alleviate the data scarcity challenge harnessing Meta-Learning, a subcategory of Machine Learning that trains models to understand and adapt to new tasks on their own. We use Meta-Learning to identify and exploit transferable patterns from data-rich cities to cities where not enough data is available to estimate the MFD. 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 MAE improvement in flow prediction of around 50% across cities (depending on the subset of loop detectors tested). The Meta-Learning framework thus successfully generalises 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. We directly test this assumption by applying the Meta-Learning outputs to unseen cities to simulate a real-life application scenario and the wide applicability of the proposed methodology. Finally, the proposed framework is validated against traditional Transfer Learning approaches and tested with FitFun, a model for FD estimation from the literature, to prove its transferability.