/NMFD_GNN

A physics-informed machine learning model for traffic state imputation

Primary LanguageHTMLMIT LicenseMIT

NMFD-GNN

  • Network Macroscopic Fundamental Diagram (NMFD) - Graph Neural Network (GNN).
  • A physics-informed machine learning model for traffic state imputation (TSI).

Error correction

【June 24, 2024】We identified an error in our paper today. The current Eq. 3 is $\tilde{A}^{fix} = (\tilde{D}^{fix})^{-1/2}\tilde{E}^{fix}(\tilde{D}^{fix})^{1/2}$, which should be correctly stated as $\tilde{A}^{fix} = (\tilde{D}^{fix})^{-1/2}\tilde{E}^{fix}(\tilde{D}^{fix})^{-1/2}$. Our codes and implementation results are correct. Please refer to the code starting from line 81 at https://github.com/JiaweiXue/NMFD_GNN/blob/main/model/nmfd_gnn.py. We apologize for any inconvenience this may have caused to our readers.

Introduction

  • TSI refers to the estimation of missing values of traffic variables, such as flow rate and traffic density, using available data.
  • This study proposes NMFD-GNN, a physics-informed machine learning model that fuses the NMFD with the GNN to perform network-wide TSI.
  • Our proposed NMFD-GNN model and its variants, NMFD-GNN-HINGE and NMFD-GNN-UPPER, are evaluated on road networks located in Zurich and London from the UTD19 dataset (https://utd19.ethz.ch/).

Directory structure

  • utils: preparing the features and labels for the TSI task.
  • model: building NMFD-GNN, NMFD-GNN-HINGE, and NMFD-GNN-UPPER models.
  • main: training and testing the model.
  • result: presenting implementation results.
  • figure: describing problems, methods, and data.

Requirements

  • Python 2.7.5 or higher.
  • Torch 2.0.0 or higher.

Paper

Network Macroscopic Fundamental Diagram-informed Graph Learning for Traffic State Imputation. Jiawei Xue, Eunhan Ka, Yiheng Feng, Satish V. Ukkusuri*, June 2024.

Poster presentation at ISTTT25; Publication on Transportation Research Part B: Methodological.

Building NMFD-GNN to perform the TSI task

NMFD-GNN = the physics module (the λ-trapezoidal MFD) + the machine learning module (the graph convolutional network)

  • The λ-trapezoidal MFD was proposed by the following study:
  • Ambühl, et al. (2020). A functional form with a physical meaning for the macroscopic fundamental diagram. Transportation Research Part B: Methodological.

Study areas in Zurich and London

MFDs

The following papers form a solid foundation for this study. We sincerely thank their contributions to the community.

Index Authors Title Publication
1 Loder, A., L. Ambühl, M. Menendez, and K. W. Axhausen Understanding traffic capacity of urban networks Scientific Reports, 2019
2 Johari, M., M. Keyvan-Ekbatani, L. Leclercq, D. Ngoduy, and H. S. Mahmassani Macroscopic network-level traffic models: Bridging fifty years of development toward the next era TR-Part C, 2021
3 Ambühl, L, A. Loder, M. C. Bliemer, M. Menendez, and K. W. Axhausen A functional form with a physical meaning for the macroscopic fundamental diagram TR-Part B, 2020
4 Zhou, J., Cui, G., Hu, S., Zhang, Z., Yang, C., Liu, Z., Wang, L., Li, C. and Sun, M Graph neural networks: A review of methods and applications AI Open, 2020
5 Liang. Y., Z. Zhao, and L. Sun Memory-augmented dynamic graph convolution networks for traffic data imputation with diverse missing patterns TR-Part C, 2022

License

MIT license