# Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting

arXiv: https://arxiv.org/abs/2305.18687 · HTML: https://mlsanity.com/paper/2305.18687/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [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)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [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)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Spatio-Temporal LSTM with Trust Gates for 3D Human Action Recognition](https://mlsanity.com/paper/1607.07043/) (2016)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Differential Recurrent Neural Networks for Action Recognition](https://mlsanity.com/paper/1504.06678/) (2015)
- [Neural Ordinary Differential Equation based Recurrent Neural Network Model](https://mlsanity.com/paper/2005.09807/) (2020)

## Built on by (most cited first, 11 of 11)

- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Towards Scene Graph Anticipation](https://mlsanity.com/paper/2403.04899/) (2024)
- [A Primer on Temporal Graph Learning](https://mlsanity.com/paper/2401.03988/) (2024)
- [Graph Neural Stochastic Differential Equations](https://mlsanity.com/paper/2308.12316/) (2023)
- [Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting](https://mlsanity.com/paper/2408.06445/) (2024)
- [Online Algorithm for Node Feature Forecasting in Temporal Graphs](https://mlsanity.com/paper/2401.16800/) (2024)
- [Spatio-Temporal Partial Sensing Forecast for Long-term Traffic](https://mlsanity.com/paper/2408.02689/) (2024)
- [Spatio-temporal Multivariate Time Series Forecast with Chosen Variables](https://mlsanity.com/paper/2510.24027/) (2025)
- [Continuous Cross-Domain Traffic State Prediction via Memory-Augmented Graph Liquid Time-Constant Networks](https://mlsanity.com/paper/2606.15807/) (2026)
- [INDEQS: Informed Neural controlled Differential EQuationS](https://mlsanity.com/paper/2606.19138/) (2026)

## Abstract (arXiv)

There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal correlations observed in traffic networks. Current works primarily rely on road networks with graph structures and learn representations using graph neural networks (GNNs), but this approach suffers from over-smoothing problem in deep architectures. To tackle this problem, recent methods introduced the combination of GNNs with residual connections or neural ordinary differential equations (ODE). However, current graph ODE models face two key limitations in feature extraction: (1) they lean towards global temporal patterns, overlooking local patterns that are important for unexpected events; and (2) they lack dynamic semantic edges in their architectural design. In this paper, we propose a novel architecture called Graph-based Multi-ODE Neural Networks (GRAM-ODE) which is designed with multiple connective ODE-GNN modules to learn better representations by capturing different views of complex local and global dynamic spatio-temporal dependencies. We also add some techniques like shared weights and divergence constraints into the intermediate layers of distinct ODE-GNN modules to further improve their communication towards the forecasting task. Our extensive set of experiments conducted on six real-world datasets demonstrate the superior performance of GRAM-ODE compared with state-of-the-art baselines as well as the contribution of different components to the overall performance. The code is available at https://github.com/zbliu98/GRAM-ODE