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Learning traffic flows: Graph Neural Networks for Metamodelling Traffic Assignment

Oskar Bohn Lassen, Serio Agriesti, Mohamed Eldafrawi, Daniele Gammelli, Guido Cantelmo, Guido Gentile, Francisco Camara Pereira

TL;DR

The paper tackles the computational burden of solving the Traffic Assignment Problem (TAP) under Stochastic User Equilibrium (SUE) by proposing a metamodel based on a Message-Passing Neural Network (MPNN) with an Encoder–MPNN–Decoder architecture. The model explicitly incorporates edge features (free-flow time, speed limit, capacity) and is trained to mimic the TAP algorithm, using ground-truth SUE data generated by a simulator for a Sioux Falls network. Through in-distribution and out-of-distribution experiments, the study shows that the MPNN can approximate equilibrium flows with competitive accuracy and demonstrates improved robustness to capacity and speed changes, though MLPs can be strong baselines when OD-demand information is directly available. The findings suggest that graph-based metamodeling enables faster, scalable, real-time scenario analysis for transportation planning, with potential gains in large networks where iterative simulations are costly.

Abstract

The Traffic Assignment Problem is a fundamental, yet computationally expensive, task in transportation modeling, especially for large-scale networks. Traditional methods require iterative simulations to reach equilibrium, making real-time or large-scale scenario analysis challenging. In this paper, we propose a learning-based approach using Message-Passing Neural Networks as a metamodel to approximate the equilibrium flow of the Stochastic User Equilibrium assignment. Our model is designed to mimic the algorithmic structure used in conventional traffic simulators allowing it to better capture the underlying process rather than just the data. We benchmark it against other conventional deep learning techniques and evaluate the model's robustness by testing its ability to predict traffic flows on input data outside the domain on which it was trained. This approach offers a promising solution for accelerating out-of-distribution scenario assessments, reducing computational costs in large-scale transportation planning, and enabling real-time decision-making.

Learning traffic flows: Graph Neural Networks for Metamodelling Traffic Assignment

TL;DR

The paper tackles the computational burden of solving the Traffic Assignment Problem (TAP) under Stochastic User Equilibrium (SUE) by proposing a metamodel based on a Message-Passing Neural Network (MPNN) with an Encoder–MPNN–Decoder architecture. The model explicitly incorporates edge features (free-flow time, speed limit, capacity) and is trained to mimic the TAP algorithm, using ground-truth SUE data generated by a simulator for a Sioux Falls network. Through in-distribution and out-of-distribution experiments, the study shows that the MPNN can approximate equilibrium flows with competitive accuracy and demonstrates improved robustness to capacity and speed changes, though MLPs can be strong baselines when OD-demand information is directly available. The findings suggest that graph-based metamodeling enables faster, scalable, real-time scenario analysis for transportation planning, with potential gains in large networks where iterative simulations are costly.

Abstract

The Traffic Assignment Problem is a fundamental, yet computationally expensive, task in transportation modeling, especially for large-scale networks. Traditional methods require iterative simulations to reach equilibrium, making real-time or large-scale scenario analysis challenging. In this paper, we propose a learning-based approach using Message-Passing Neural Networks as a metamodel to approximate the equilibrium flow of the Stochastic User Equilibrium assignment. Our model is designed to mimic the algorithmic structure used in conventional traffic simulators allowing it to better capture the underlying process rather than just the data. We benchmark it against other conventional deep learning techniques and evaluate the model's robustness by testing its ability to predict traffic flows on input data outside the domain on which it was trained. This approach offers a promising solution for accelerating out-of-distribution scenario assessments, reducing computational costs in large-scale transportation planning, and enabling real-time decision-making.
Paper Structure (22 sections, 11 equations, 4 figures, 1 table)

This paper contains 22 sections, 11 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation and theoretical background
  3. The Traffic Assignment Problem
  4. Graph Neural Networks
  5. Methodology
  6. Input Representation
  7. Encoder
  8. MPNN
  9. Decoder
  10. Loss Function
  11. Experiments
  12. Dataset
  13. Data Preprocessing and Cleaning
  14. Out-of-distribution data generation
  15. Training and Evaluation
  16. ...and 7 more sections

Figures (4)

  • Figure 1: Mean absolute error (MAE) of all models per edge. The performance of the MLP and GatedGCN is best across all edges. Noticeably, some edges have lower MAE where the GCN and mean comparison
  • Figure 2: Mean absolute error across all models when changing x% of the links to up to 25% out-of-distribution speed limits.
  • Figure 3: Mean absolute error across all models when changing x% of the links to up to 25% out-of-distribution capacities.
  • Figure 4: Mean absolute error across all models when changing x% of the nodes to up to 25% out-of-distribution demand flows.