mlsanityData to 14 Oct 2026

Graph Neural Controlled Differential Equations for Traffic Forecasting

arXiv 2112.03558 ↗First posted 7 Dec 2021cs.LG cs.AIcited by 133

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Abstract (arXiv)

Traffic forecasting is one of the most popular spatio-temporal tasks in the field of machine learning. A prevalent approach in the field is to combine graph convolutional networks and recurrent neural networks for the spatio-temporal processing. There has been fierce competition and many novel methods have been proposed. In this paper, we present the method of spatio-temporal graph neural controlled differential equation (STG-NCDE). Neural controlled differential equations (NCDEs) are a breakthrough concept for processing sequential data. We extend the concept and design two NCDEs: one for the temporal processing and the other for the spatial processing. After that, we combine them into a single framework. We conduct experiments with 6 benchmark datasets and 20 baselines. STG-NCDE shows the best accuracy in all cases, outperforming all those 20 baselines by non-trivial margins.

Key facts. Cited by 133 papers in the map (data through 14 Oct 2026). Builds on 15 of its 42 references that are in the map. First posted on arXiv 7 Dec 2021.

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15 of 42 references.

References · 15

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  3. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  4. 2018An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modelingcited by 1,476
  5. 2015Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcastingcited by 1,436
  6. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,136
  7. 2019Graph WaveNet for Deep Spatial-Temporal Graph Modelingcited by 829
  8. 2020Adaptive Graph Convolutional Recurrent Network for Traffic Forecastingcited by 530
  9. 2020Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecastingcited by 213
  10. 2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 210
  11. 2017Deep Learning for Precipitation Nowcasting: A Benchmark and A New Modelcited by 182
  12. 2021Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecastingcited by 67
3 more
  1. 2019STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecastingcited by 60
  2. 2016Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasetscited by 31
  3. 2018Exascale Deep Learning for Climate Analyticscited by 28

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 12; 2023: 47; 2024: 38; 2025: 19; 2026: 17.

133 papers.

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  1. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  2. 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
  3. 2023PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Predictioncited by 137
  4. 2023LargeST: A Benchmark Dataset for Large-Scale Traffic Forecastingcited by 118
  5. 2023Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysiscited by 117
  6. 2024Spatial-Temporal Large Language Model for Traffic Predictioncited by 83
  7. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
  8. 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
  9. 2023A Comprehensive Survey on Deep Graph Representation Learningcited by 72
  10. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  11. 2023PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputationcited by 66
  12. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 65
38 more
  1. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  2. 2023DSformer: A Double Sampling Transformer for Multivariate Time Series Long-term Predictioncited by 49
  3. 2023Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatmentcited by 47
  4. 2023Graph Deep Learning for Time Series Forecastingcited by 26
  5. 2024Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspectivecited by 26
  6. 2023Cross-city Few-Shot Traffic Forecasting via Traffic Pattern Bankcited by 24
  7. 2024STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Modelcited by 24
  8. 2023Do We Really Need Graph Neural Networks for Traffic Forecasting?cited by 20
  9. 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learningcited by 20
  10. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  11. 2023Disentangling Structured Components: Towards Adaptive, Interpretable and Scalable Time Series Forecastingcited by 19
  12. 2025Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecastingcited by 19
  13. 2024Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Seriescited by 15
  14. 2022Spatial-Temporal Interactive Dynamic Graph Convolution Network for Traffic Forecastingcited by 14
  15. 2023Graph Neural Rough Differential Equations for Traffic Forecastingcited by 14
  16. 2023Localised Adaptive Spatial-Temporal Graph Neural Networkcited by 14
  17. 2023Dynamic Hypergraph Structure Learning for Traffic Flow Forecastingcited by 14
  18. 2024A Survey of Generative Techniques for Spatial-Temporal Data Miningcited by 14
  19. 2024Agentic Retrieval-Augmented Generation for Time Series Analysiscited by 14
  20. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  21. 2023Explainable Spatio-Temporal Graph Neural Networkscited by 13
  22. 2022Enhancing the Robustness via Adversarial Learning and Joint Spatial-Temporal Embeddings in Traffic Forecastingcited by 11
  23. 2023Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecastingcited by 11
  24. 2023Spatio-Temporal Meta Contrastive Learningcited by 11
  25. 2024Unveiling Delay Effects in Traffic Forecasting: A Perspective from Spatial-Temporal Delay Differential Equationscited by 11
  26. 2024Temporal Graph ODEs for Irregularly-Sampled Time Seriescited by 11
  27. 2023LaDe: The First Comprehensive Last-mile Delivery Dataset from Industrycited by 10
  28. 2024Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Valuescited by 10
  29. 2024Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graphcited by 10
  30. 2024STGformer: Efficient Spatiotemporal Graph Transformer for Traffic Forecastingcited by 9
  31. 2024A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classificationcited by 9
  32. 2023Learnable Path in Neural Controlled Differential Equationscited by 8
  33. 2023Learning Informative Representation for Fairness-aware Multivariate Time-series Forecasting: A Group-based Perspectivecited by 8
  34. 2023Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecastingcited by 8
  35. 2023STG4Traffic: A Survey and Benchmark of Spatial-Temporal Graph Neural Networks for Traffic Predictioncited by 8
  36. 2022TimeKit: A Time-series Forecasting-based Upgrade Kit for Collaborative Filteringcited by 7
  37. 2023Learning Dynamic Graph Embeddings with Neural Controlled Differential Equationscited by 7
  38. 2023ChatTraffic: Text-to-Traffic Generation via Diffusion Modelcited by 7

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