# Graph Neural Rough Differential Equations for Traffic Forecasting

arXiv: https://arxiv.org/abs/2303.10909 · HTML: https://mlsanity.com/paper/2303.10909/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 73 references that are in the map.
- First posted on arXiv 20 Mar 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (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)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [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)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting](https://mlsanity.com/paper/2105.04100/) (2021)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)
- [Predicting Path Failure In Time-Evolving Graphs](https://mlsanity.com/paper/1905.03994/) (2019)
- [GREAD: Graph Neural Reaction-Diffusion Networks](https://mlsanity.com/paper/2211.14208/) (2022)
- [Traffic Flow Forecasting with Spatial-Temporal Graph Diffusion Network](https://mlsanity.com/paper/2110.04038/) (2021)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasets](https://mlsanity.com/paper/1605.01156/) (2016)
- [Exascale Deep Learning for Climate Analytics](https://mlsanity.com/paper/1810.01993/) (2018)
- [Climate Modeling with Neural Diffusion Equations](https://mlsanity.com/paper/2111.06011/) (2021)
- [Two-stage Training of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2011.05097/) (2020)
- [Numerical Weather Forecasting using Convolutional-LSTM with Attention and Context Matcher Mechanisms](https://mlsanity.com/paper/2102.00696/) (2021)

## Built on by (most cited first, 14 of 14)

- [PANDA: Expanded Width-Aware Message Passing Beyond Rewiring](https://mlsanity.com/paper/2406.03671/) (2024)
- [Continuous-time Autoencoders for Regular and Irregular Time Series Imputation](https://mlsanity.com/paper/2312.16581/) (2023)
- [Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning](https://mlsanity.com/paper/2506.20324/) (2025)
- [Variational Mode-Driven Graph Convolutional Network for Spatiotemporal Traffic Forecasting](https://mlsanity.com/paper/2408.16191/) (2024)
- [Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations](https://mlsanity.com/paper/2311.04522/) (2023)
- [Bridging Dynamic Factor Models and Neural Controlled Differential Equations for Nowcasting GDP](https://mlsanity.com/paper/2409.08732/) (2024)
- [Deep Signature: Characterization of Large-Scale Molecular Dynamics](https://mlsanity.com/paper/2410.02847/) (2024)
- [ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations](https://mlsanity.com/paper/2411.01267/) (2024)
- [MHGNet: Multi-Heterogeneous Graph Neural Network for Traffic Prediction](https://mlsanity.com/paper/2501.03635/) (2025)
- [FacePhys: State of the Heart Learning](https://mlsanity.com/paper/2512.06275/) (2025)
- [Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs](https://mlsanity.com/paper/2605.30213/) (2026)
- [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)
- [STHMoE: Hypergraph-Enhanced Heterogeneous Dependency Coordination for LLM-Based Urban Traffic Data Forecasting](https://mlsanity.com/paper/2609.15172/) (2026)

## 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 rough differential equation (STG-NRDE). Neural rough differential equations (NRDEs) are a breakthrough concept for processing time-series data. Their main concept is to use the log-signature transform to convert a time-series sample into a relatively shorter series of feature vectors. We extend the concept and design two NRDEs: 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 27 baselines. STG-NRDE shows the best accuracy in all cases, outperforming all those 27 baselines by non-trivial margins.