PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction
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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
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- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2021Swin Transformer: Hierarchical Vision Transformer using Shifted Windowscited by 12,082
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Decoupled Weight Decay Regularizationcited by 1,722
- 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,125
- 2019Graph WaveNet for Deep Spatial-Temporal Graph Modelingcited by 820
- 2020Benchmarking Graph Neural Networkscited by 672
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- 2020Adaptive Graph Convolutional Recurrent Network for Traffic Forecastingcited by 525
15 more
- 2019GMAN: A Graph Multi-Attention Network for Traffic Predictioncited by 433
- 2016Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Predictioncited by 330
- 2020Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecastingcited by 212
- 2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 209
- 2020Spatial-Temporal Transformer Networks for Traffic Flow Forecastingcited by 179
- 2018Deep Multi-View Spatial-Temporal Network for Taxi Demand Predictioncited by 162
- 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
- 2019Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecastingcited by 69
- 2022Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semanticscited by 58
- 2020Coupled Layer-wise Graph Convolution for Transportation Demand Predictioncited by 54
- 2021Traffic Flow Forecasting with Spatial-Temporal Graph Diffusion Networkcited by 52
- 2022STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Predictioncited by 45
- 2020Preserving Dynamic Attention for Long-Term Spatial-Temporal Predictioncited by 30
- 2020FC-GAGA: Fully Connected Gated Graph Architecture for Spatio-Temporal Traffic Forecastingcited by 30
- 2021Learning dynamic and hierarchical traffic spatiotemporal features with Transformercited by 26
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Citing papers per year: 2023: 15; 2024: 46; 2025: 43; 2026: 31.
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- 2023Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysiscited by 113
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- 2024Towards Explainable Traffic Flow Prediction with Large Language Modelscited by 20
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- 2024STD-PLM: Understanding Both Spatial and Temporal Properties of Spatial-Temporal Data with PLMcited by 9
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- 2024UniFlow: A Foundation Model for Unified Urban Spatio-Temporal Flow Predictioncited by 7
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- 2024ST-MambaSync: The Complement of Mamba and Transformers for Spatial-Temporal in Traffic Flow Predictioncited by 2
- 2025Damba-ST: Domain-Adaptive Mamba for Efficient Urban Spatio-Temporal Predictioncited by 2
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- 2026GAMMA-Net: Adaptive Long-Horizon Traffic Spatio-Temporal Forecasting Model based on Interleaved Graph Attention and Multi-Axis Mambacited by 1
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- 2024ST-Mamba: Spatial-Temporal Selective State Space Model for Traffic Flow Prediction20 Apr 2024
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- 2024DiffLight: A Partial Rewards Conditioned Diffusion Model for Traffic Signal Control with Missing Data30 Oct 2024
- 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Data29 Apr 2024
- 2023ChatTraffic: Text-to-Traffic Generation via Diffusion Model27 Nov 2023
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- 2024Spatial-Temporal Large Language Model for Traffic Predictioncited by 81
- 2024How Can Large Language Models Understand Spatial-Temporal Data?cited by 31
- 2023Mixture-of-Linear-Experts for Long-term Time Series Forecastingcited by 29
- 2023Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecastingcited by 27
- 2024OpenCity: Open Spatio-Temporal Foundation Models for Traffic Predictioncited by 27
- 2024Towards Explainable Traffic Flow Prediction with Large Language Modelscited by 20
- 2023Irregular Traffic Time Series Forecasting Based on Asynchronous Spatio-Temporal Graph Convolutional Networkcited by 19
- 2024FlashST: A Simple and Universal Prompt-Tuning Framework for Traffic Predictioncited by 18
- 2024BIGCity: A Universal Spatiotemporal Model for Unified Trajectory and Traffic State Data Analysiscited by 16
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- 2026Addressing Spatial Indistinguishability in Spatiotemporal Prediction via Optimal Transport-Guided Masking28 Sep 2026
- 2026Learning Local Heterogeneity and Cross-Region Context for Large-Scale Traffic Forecasting23 Sep 2026
- 2026Toward Equitable Low-Carbon Mobility: Fairness-Aware Demand Prediction for Expanding Bike-Sharing Systems26 Aug 2026
- 2026F2STNet: Fair and Federated Spectral-Temporal Modeling for Graph Forecasting10 Aug 2026
- 2026Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting5 Aug 2026
- 2026DSETA: A Dual-Stage Continual Learning Framework for Travel Time Prediction in Dynamic Traffic Environments1 Aug 2026
- 2026Revisiting the Adversarial Robustness of Graph-Based Traffic Forecasting30 Jul 2026
- 2026Neural Architecture Search for Traffic Prediction: A Survey of Methods, Challenges, and Future Directions29 Jul 2026
- 2026Scene-Conditioned Relation Routing for urban cellular activity forecasting25 Jul 2026
- 2026EMAGN: Efficient Multi-Attention Graph Network via Learned Clustering for Scalable Traffic Forecasting14 Jul 2026
- 2026Do We Really Need Adaptive Global Spatial Attention for Traffic Forecasting?14 Jul 2026
- 2026Frequency-Domain Multi-Modality Transportation Modeling9 Jul 2026
12 newest of 118 All 118 (JSON)