# End-to-End Heterogeneous Graph Neural Networks for Traffic Assignment

arXiv: https://arxiv.org/abs/2310.13193 · HTML: https://mlsanity.com/paper/2310.13193/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [MAGNN: Metapath Aggregated Graph Neural Network for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2002.01680/) (2020)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Missing Data Reconstruction in Remote Sensing image with a Unified Spatial-Temporal-Spectral Deep Convolutional Neural Network](https://mlsanity.com/paper/1802.08369/) (2018)
- [Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filter](https://mlsanity.com/paper/1905.00406/) (2019)
- [Data-Driven Traffic Assignment: A Novel Approach for Learning Traffic Flow Patterns Using a Graph Convolutional Neural Network](https://mlsanity.com/paper/2202.10508/) (2022)
- [Graph Neural Network Surrogate for Seismic Reliability Analysis of Highway Bridge Systems](https://mlsanity.com/paper/2210.06404/) (2022)
- [A hybrid deep-learning-metaheuristic framework for bi-level network design problems](https://mlsanity.com/paper/2303.06024/) (2023)

## Built on by (most cited first, 13 of 13)

- [Multi-Class Traffic Assignment using Multi-View Heterogeneous Graph Attention Networks](https://mlsanity.com/paper/2501.09117/) (2025)
- [Learning traffic flows: Graph Neural Networks for Metamodelling Traffic Assignment](https://mlsanity.com/paper/2505.11230/) (2025)
- [Heterogeneous Graph Sequence Neural Networks for Dynamic Traffic Assignment](https://mlsanity.com/paper/2408.04131/) (2024)
- [Graph Neural Networks for Travel Distance Estimation and Route Recommendation Under Probabilistic Hazards](https://mlsanity.com/paper/2501.09803/) (2025)
- [GAMDTP: Dynamic Trajectory Prediction with Graph Attention Mamba Network](https://mlsanity.com/paper/2504.04862/) (2025)
- [Reinforcement Learning-based Sequential Route Recommendation for System-Optimal Traffic Assignment](https://mlsanity.com/paper/2505.20889/) (2025)
- [Scalable and Reliable Multi-agent Reinforcement Learning for Traffic Assignment](https://mlsanity.com/paper/2506.17029/) (2025)
- [Supply Chain Network Extraction and Entity Classification Leveraging Large Language Models](https://mlsanity.com/paper/2410.13051/) (2024)
- [From Optimization to Prediction: Transformer-Based Path-Flow Estimation to the Traffic Assignment Problem](https://mlsanity.com/paper/2510.19889/) (2025)
- [Metalearning traffic assignment for network disruptions with graph convolutional neural networks](https://mlsanity.com/paper/2603.06763/) (2026)
- [Beyond Feature and Structure Alignment: Learning Transferable Propagation Knowledge for Graph Foundation Models](https://mlsanity.com/paper/2607.28980/) (2026)
- [Learning from user's behaviour of some well-known congested traffic networks](https://mlsanity.com/paper/2508.14804/) (2025)
- [GUIDED Network-Agnostic Feature Initialization for Spatial Transferability in GNN-based Models](https://mlsanity.com/paper/2607.19270/) (2026)

## Abstract (arXiv)

The traffic assignment problem is one of the significant components of traffic flow analysis for which various solution approaches have been proposed. However, deploying these approaches for large-scale networks poses significant challenges. In this paper, we leverage the power of heterogeneous graph neural networks to propose a novel end-to-end surrogate model for traffic assignment, specifically user equilibrium traffic assignment problems. Our model integrates an adaptive graph attention mechanism with auxiliary "virtual" links connecting origin-destination node pairs, This integration enables the model to capture spatial traffic patterns across different links, By incorporating the node-based flow conservation law into the overall loss function, the model ensures the prediction results in compliance with flow conservation principles, resulting in highly accurate predictions for both link flow and flow-capacity ratios. We present numerical experiments on urban transportation networks and show that the proposed heterogeneous graph neural network model outperforms other conventional neural network models in terms of convergence rate and prediction accuracy. Notably, by introducing two different training strategies, the proposed heterogeneous graph neural network model can also be generalized to different network topologies. This approach offers a promising solution for complex traffic flow analysis and prediction, enhancing our understanding and management of a wide range of transportation systems.