# From Optimization to Prediction: Transformer-Based Path-Flow Estimation to the Traffic Assignment Problem

arXiv: https://arxiv.org/abs/2510.19889 · HTML: https://mlsanity.com/paper/2510.19889/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Deep Forecast: Deep Learning-based Spatio-Temporal Forecasting](https://mlsanity.com/paper/1707.08110/) (2017)
- [End-to-End Heterogeneous Graph Neural Networks for Traffic Assignment](https://mlsanity.com/paper/2310.13193/) (2023)
- [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)
- [Multi-Class Traffic Assignment using Multi-View Heterogeneous Graph Attention Networks](https://mlsanity.com/paper/2501.09117/) (2025)
- [Network Level Spatial Temporal Traffic State Forecasting with Hierarchical-Attention-LSTM (HierAttnLSTM)](https://mlsanity.com/paper/2201.05760/) (2022)
- [A Structure-Aware Lane Graph Transformer Model for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2405.20121/) (2024)
- [A Distributed Gradient Approach for System Optimal Dynamic Traffic Assignment](https://mlsanity.com/paper/2112.14389/) (2021)

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

- [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 essential for traffic flow analysis, traditionally solved using mathematical programs under the Equilibrium principle. These methods become computationally prohibitive for large-scale networks due to non-linear growth in complexity with the number of OD pairs. This study introduces a novel data-driven approach using deep neural networks, specifically leveraging the Transformer architecture, to predict equilibrium path flows directly. By focusing on path-level traffic distribution, the proposed model captures intricate correlations between OD pairs, offering a more detailed and flexible analysis compared to traditional link-level approaches. The Transformer-based model drastically reduces computation time, while adapting to changes in demand and network structure without the need for recalculation. Numerical experiments are conducted on the Manhattan-like synthetic network, the Sioux Falls network, and the Eastern-Massachusetts network. The results demonstrate that the proposed model is orders of magnitude faster than conventional optimization. It efficiently estimates path-level traffic flows in multi-class networks, reducing computational costs and improving prediction accuracy by capturing detailed trip and flow information. The model also adapts flexibly to varying demand and network conditions, supporting traffic management and enabling rapid `what-if' analyses for enhanced transportation planning and policy-making.