# Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting

arXiv: https://arxiv.org/abs/2106.12931 · HTML: https://mlsanity.com/paper/2106.12931/

## Key facts

- Cited by 210 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 24 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [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)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels](https://mlsanity.com/paper/2104.02995/) (2021)
- [Graph Structural-topic Neural Network](https://mlsanity.com/paper/2006.14278/) (2020)

## Built on by (most cited first, 30 of 210)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [A Unified Replay-based Continuous Learning Framework for Spatio-Temporal Prediction on Streaming Data](https://mlsanity.com/paper/2404.14999/) (2024)
- [Domain Adversarial Spatial-Temporal Network: A Transferable Framework for Short-term Traffic Forecasting across Cities](https://mlsanity.com/paper/2202.03630/) (2022)
- [How Can Large Language Models Understand Spatial-Temporal Data?](https://mlsanity.com/paper/2401.14192/) (2024)
- [Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecasting](https://mlsanity.com/paper/2312.00516/) (2023)
- [OpenCity: Open Spatio-Temporal Foundation Models for Traffic Prediction](https://mlsanity.com/paper/2408.10269/) (2024)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspective](https://mlsanity.com/paper/2412.09972/) (2024)
- [Cross-city Few-Shot Traffic Forecasting via Traffic Pattern Bank](https://mlsanity.com/paper/2308.09727/) (2023)
- [Do We Really Need Graph Neural Networks for Traffic Forecasting?](https://mlsanity.com/paper/2301.12603/) (2023)
- [Irregular Traffic Time Series Forecasting Based on Asynchronous Spatio-Temporal Graph Convolutional Network](https://mlsanity.com/paper/2308.16818/) (2023)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [Towards Explainable Traffic Flow Prediction with Large Language Models](https://mlsanity.com/paper/2404.02937/) (2024)
- [Disentangling Structured Components: Towards Adaptive, Interpretable and Scalable Time Series Forecasting](https://mlsanity.com/paper/2305.13036/) (2023)
- [Building Transportation Foundation Model via Generative Graph Transformer](https://mlsanity.com/paper/2305.14826/) (2023)
- [Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting](https://mlsanity.com/paper/2502.12213/) (2025)
- [Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecasting](https://mlsanity.com/paper/2405.10800/) (2024)
- [FlashST: A Simple and Universal Prompt-Tuning Framework for Traffic Prediction](https://mlsanity.com/paper/2405.17898/) (2024)
- [BACKTIME: Backdoor Attacks on Multivariate Time Series Forecasting](https://mlsanity.com/paper/2410.02195/) (2024)
- [RPMixer: Shaking Up Time Series Forecasting with Random Projections for Large Spatial-Temporal Data](https://mlsanity.com/paper/2402.10487/) (2024)
- [Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting](https://mlsanity.com/paper/2305.09703/) (2023)

## Abstract (arXiv)

Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring it to a most intractable challenge. Existing works typically utilize shallow graph convolution networks (GNNs) and temporal extracting modules to model spatial and temporal dependencies respectively. However, the representation ability of such models is limited due to: (1) shallow GNNs are incapable to capture long-range spatial correlations, (2) only spatial connections are considered and a mass of semantic connections are ignored, which are of great importance for a comprehensive understanding of traffic networks. To this end, we propose Spatial-Temporal Graph Ordinary Differential Equation Networks (STGODE). Specifically, we capture spatial-temporal dynamics through a tensor-based ordinary differential equation (ODE), as a result, deeper networks can be constructed and spatial-temporal features are utilized synchronously. To understand the network more comprehensively, semantical adjacency matrix is considered in our model, and a well-design temporal dialated convolution structure is used to capture long term temporal dependencies. We evaluate our model on multiple real-world traffic datasets and superior performance is achieved over state-of-the-art baselines.