# STR-GODEs: Spatial-Temporal-Ridership Graph ODEs for Metro Ridership Prediction

arXiv: https://arxiv.org/abs/2107.04980 · HTML: https://mlsanity.com/paper/2107.04980/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 45 references that are in the map.
- First posted on arXiv 11 Jul 2021.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [STEER: Simple Temporal Regularization For Neural ODEs](https://mlsanity.com/paper/2006.10711/) (2020)
- [ODE2VAE: Deep generative second order ODEs with Bayesian neural networks](https://mlsanity.com/paper/1905.10994/) (2019)
- [Model-based Reinforcement Learning for Semi-Markov Decision Processes with Neural ODEs](https://mlsanity.com/paper/2006.16210/) (2020)
- [Attentive Crowd Flow Machines](https://mlsanity.com/paper/1809.00101/) (2018)

## Built on by (most cited first, 1 of 1)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)

## Abstract (arXiv)

The metro ridership prediction has always received extensive attention from governments and researchers. Recent works focus on designing complicated graph convolutional recurrent network architectures to capture spatial and temporal patterns. These works extract the information of spatial dimension well, but the limitation of temporal dimension still exists. We extended Neural ODE algorithms to the graph network and proposed the STR-GODEs network, which can effectively learn spatial, temporal, and ridership correlations without the limitation of dividing data into equal-sized intervals on the timeline. While learning the spatial relations and the temporal correlations, we modify the GODE-RNN cell to obtain the ridership feature and hidden states. Ridership information and its hidden states are added to the GODESolve to reduce the error accumulation caused by long time series in prediction. Extensive experiments on two large-scale datasets demonstrate the efficacy and robustness of our model.