mlsanityData to 7 Oct 2026

PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction

arXiv 2301.07945 ↗First posted 19 Jan 2023cs.LGcited by 135

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Abstract (arXiv)

As a core technology of Intelligent Transportation System, traffic flow prediction has a wide range of applications. The fundamental challenge in traffic flow prediction is to effectively model the complex spatial-temporal dependencies in traffic data. Spatial-temporal Graph Neural Network (GNN) models have emerged as one of the most promising methods to solve this problem. However, GNN-based models have three major limitations for traffic prediction: i) Most methods model spatial dependencies in a static manner, which limits the ability to learn dynamic urban traffic patterns; ii) Most methods only consider short-range spatial information and are unable to capture long-range spatial dependencies; iii) These methods ignore the fact that the propagation of traffic conditions between locations has a time delay in traffic systems. To this end, we propose a novel Propagation Delay-aware dynamic long-range transFormer, namely PDFormer, for accurate traffic flow prediction. Specifically, we design a spatial self-attention module to capture the dynamic spatial dependencies. Then, two graph masking matrices are introduced to highlight spatial dependencies from short- and long-range views. Moreover, a traffic delay-aware feature transformation module is proposed to empower PDFormer with the capability of explicitly modeling the time delay of spatial information propagation. Extensive experimental results on six real-world public traffic datasets show that our method can not only achieve state-of-the-art performance but also exhibit competitive computational efficiency. Moreover, we visualize the learned spatial-temporal attention map to make our model highly interpretable.

Key facts. Cited by 135 papers in the map (data through 7 Oct 2026). Builds on 27 of its 54 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

27 of 54 references.

References · 27

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  3. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  4. 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
  5. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  6. 2017Decoupled Weight Decay Regularizationcited by 1,722
  7. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,125
  8. 2019Graph WaveNet for Deep Spatial-Temporal Graph Modelingcited by 820
  9. 2020Benchmarking Graph Neural Networkscited by 672
  10. 2020A Generalization of Transformer Networks to Graphscited by 653
  11. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 563
  12. 2020Adaptive Graph Convolutional Recurrent Network for Traffic Forecastingcited by 525
15 more
  1. 2019GMAN: A Graph Multi-Attention Network for Traffic Predictioncited by 433
  2. 2016Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Predictioncited by 330
  3. 2020Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecastingcited by 212
  4. 2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 209
  5. 2020Spatial-Temporal Transformer Networks for Traffic Flow Forecastingcited by 179
  6. 2018Deep Multi-View Spatial-Temporal Network for Taxi Demand Predictioncited by 162
  7. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  8. 2019Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecastingcited by 69
  9. 2022Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semanticscited by 58
  10. 2020Coupled Layer-wise Graph Convolution for Transportation Demand Predictioncited by 54
  11. 2021Traffic Flow Forecasting with Spatial-Temporal Graph Diffusion Networkcited by 52
  12. 2022STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Predictioncited by 45
  13. 2020Preserving Dynamic Attention for Long-Term Spatial-Temporal Predictioncited by 30
  14. 2020FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecastingcited by 30
  15. 2021Learning dynamic and hierarchical traffic spatiotemporal features with Transformercited by 26

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 15; 2024: 46; 2025: 43; 2026: 31.

135 papers.

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  1. 2023Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysiscited by 113
  2. 2024Spatial-Temporal Large Language Model for Traffic Predictioncited by 81
  3. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 66
  4. 2024How Can Large Language Models Understand Spatial-Temporal Data?cited by 31
  5. 2023Mixture-of-Linear-Experts for Long-term Time Series Forecastingcited by 29
  6. 2023Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecastingcited by 27
  7. 2024OpenCity: Open Spatio-Temporal Foundation Models for Traffic Predictioncited by 27
  8. 2024STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Modelcited by 24
  9. 2024Towards Explainable Traffic Flow Prediction with Large Language Modelscited by 20
  10. 2023Irregular Traffic Time Series Forecasting Based on Asynchronous Spatio-Temporal Graph Convolutional Networkcited by 19
  11. 2024FlashST: A Simple and Universal Prompt-Tuning Framework for Traffic Predictioncited by 18
  12. 2024BIGCity: A Universal Spatiotemporal Model for Unified Trajectory and Traffic State Data Analysiscited by 16
38 more
  1. 2024A Survey of Generative Techniques for Spatial-Temporal Data Miningcited by 14
  2. 2023STAEformer: Spatio-Temporal Adaptive Embedding Makes Vanilla Transformer SOTA for Traffic Forecastingcited by 12
  3. 2024Online Test-Time Adaptation of Spatial-Temporal Traffic Flow Forecastingcited by 11
  4. 2024Diffusion Transformers as Open-World Spatiotemporal Foundation Modelscited by 10
  5. 2024STD-PLM: Understanding Both Spatial and Temporal Properties of Spatial-Temporal Data with PLMcited by 9
  6. 2024STGformer: Efficient Spatiotemporal Graph Transformer for Traffic Forecastingcited by 9
  7. 2024A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classificationcited by 9
  8. 2024Full Bayesian Significance Testing for Neural Networkscited by 8
  9. 2023ChatTraffic: Text-to-Traffic Generation via Diffusion Modelcited by 7
  10. 2024SpoT-Mamba: Learning Long-Range Dependency on Spatio-Temporal Graphs with Selective State Spacescited by 7
  11. 2024UniFlow: A Foundation Model for Unified Urban Spatio-Temporal Flow Predictioncited by 7
  12. 2024XXLTraffic: Expanding and Extremely Long Traffic forecasting beyond test adaptationcited by 6
  13. 2024CCDSReFormer: Traffic Flow Prediction with a Criss-Crossed Dual-Stream Enhanced Rectified Transformer Modelcited by 5
  14. 2025Dynamic Trend Fusion Module for Traffic Flow Predictioncited by 5
  15. 2025Generative AI for Self-Adaptive Systems: State of the Art and Research Roadmapcited by 5
  16. 2024STMGF: An Effective Spatial-Temporal Multi-Granularity Framework for Traffic Forecastingcited by 4
  17. 2024UniTE: A Survey and Unified Pipeline for Pre-training Spatiotemporal Trajectory Embeddingscited by 4
  18. 2024DiffLight: A Partial Rewards Conditioned Diffusion Model for Traffic Signal Control with Missing Datacited by 4
  19. 2024DualCast: A Model to Disentangle Aperiodic Events from Traffic Seriescited by 4
  20. 2025How Different from the Past? Spatio-Temporal Time Series Forecasting with Self-Supervised Deviation Learningcited by 4
  21. 2023Enhancing Spatiotemporal Traffic Prediction through Urban Human Activity Analysiscited by 3
  22. 2023TimelyGPT: Extrapolatable Transformer Pre-training for Long-term Time-Series Forecasting in Healthcarecited by 3
  23. 2024ST-RetNet: A Long-term Spatial-Temporal Traffic Flow Prediction Methodcited by 3
  24. 2024RAM: Replace Attention with MLP for Efficient Multivariate Time Series Forecastingcited by 3
  25. 2024A Comparative Study on Dynamic Graph Embedding based on Mamba and Transformerscited by 3
  26. 2025Multi-Source Urban Traffic Flow Forecasting with Drone and Loop Detector Datacited by 3
  27. 2025TacticExpert: Spatial-Temporal Graph Language Model for Basketball Tacticscited by 3
  28. 2025Spatiotemporal Causal Decoupling Model for Air Quality Forecastingcited by 3
  29. 2023ICN: Interactive Convolutional Network for Forecasting Travel Demand of Shared Micromobilitycited by 2
  30. 2023Unified Data Management and Comprehensive Performance Evaluation for Urban Spatial-Temporal Prediction [Experiment, Analysis & Benchmark]cited by 2
  31. 2024A novel hybrid time-varying graph neural network for traffic flow forecastingcited by 2
  32. 2024Enhancing Topological Dependencies in Spatio-Temporal Graphs with Cycle Message Passing Blockscited by 2
  33. 2024COOL: A Conjoint Perspective on Spatio-Temporal Graph Neural Network for Traffic Forecastingcited by 2
  34. 2024ST-MambaSync: The Complement of Mamba and Transformers for Spatial-Temporal in Traffic Flow Predictioncited by 2
  35. 2024TrafficGPT: Towards Multi-Scale Traffic Analysis and Generation with Spatial-Temporal Agent Frameworkcited by 2
  36. 2024FredNormer: Frequency Domain Normalization for Non-stationary Time Series Forecastingcited by 2
  37. 2024PreMixer: MLP-Based Pre-training Enhanced MLP-Mixers for Large-scale Traffic Forecastingcited by 2
  38. 2025T-Graphormer: Using Transformers for Spatiotemporal Forecastingcited by 2

50 most cited of 135 All 135 (JSON)