# Continuously Evolving Graph Neural Controlled Differential Equations for Traffic Forecasting

arXiv: https://arxiv.org/abs/2401.14695 · HTML: https://mlsanity.com/paper/2401.14695/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 26 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [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)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [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)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [DL-Traff: Survey and Benchmark of Deep Learning Models for Urban Traffic Prediction](https://mlsanity.com/paper/2108.09091/) (2021)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [Multi-View Spatial-Temporal Graph Convolutional Networks with Domain Generalization for Sleep Stage Classification](https://mlsanity.com/paper/2109.01824/) (2021)
- ["Hey, that's not an ODE": Faster ODE Adjoints via Seminorms](https://mlsanity.com/paper/2009.09457/) (2020)
- [New directions in the applications of rough path theory](https://mlsanity.com/paper/2302.04586/) (2023)
- [DSTCGCN: Learning Dynamic Spatial-Temporal Cross Dependencies for Traffic Forecasting](https://mlsanity.com/paper/2307.00518/) (2023)

## Built on by (most cited first, 2 of 2)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics](https://mlsanity.com/paper/2606.14313/) (2026)

## Abstract (arXiv)

As a crucial technique for developing a smart city, traffic forecasting has become a popular research focus in academic and industrial communities for decades. This task is highly challenging due to complex and dynamic spatial-temporal dependencies in traffic networks. Existing works ignore continuous temporal dependencies and spatial dependencies evolving over time. In this paper, we propose Continuously Evolving Graph Neural Controlled Differential Equations (CEGNCDE) to capture continuous temporal dependencies and spatial dependencies over time simultaneously. Specifically, a continuously evolving graph generator (CEGG) based on NCDE is introduced to generate the spatial dependencies graph that continuously evolves over time from discrete historical observations. Then, a graph neural controlled differential equations (GNCDE) framework is introduced to capture continuous temporal dependencies and spatial dependencies over time simultaneously. Extensive experiments demonstrate that CEGNCDE outperforms the SOTA methods by average 2.34% relative MAE reduction, 0.97% relative RMSE reduction, and 3.17% relative MAPE reduction.