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🌟 If you find this resource helpful, please consider to star this repository and cite our research:

@article{jin2025expressive,
  title={Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecasting},
  author={Ming Jin and Guangsi Shi and Yuan-Fang Li and Bo Xiong and Tian Zhou and Flora D. Salim and Liang Zhao and Lingfei Wu and Qingsong Wen and Shirui Pan},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year={2025}
}
}

Existing message-passing-based spatio-temporal GNNs (MP-STGNNS) often struggle with capturing complex, dynamic relationships in time series data, and their limitations stem from a lack of expressiveness, which we define as the ability to accurately represent a wide range of temporal and spatial dependencies within the data.

Spectral-temporal GNNs, as an advanced abstraction of MP-STGNNS, shed light on modeling differently signed time series correlations by approximating graph convolutions with a broad range of graph spectral filters beyond low-pass filtering.

In this research, we establish a framework that unravels the expressive power of spectral-temporal GNNs. To make our findings useful in practice on valid instantiations, we discuss related constraints in detail and outline a theoretical blueprint for designing spatial and temporal modules in spectral domains.

Building on these insights and to demonstrate how powerful spectral-temporal GNNs are based on our framework, we propose a simple instantiation named Temporal Graph Gegenbauer Convolution (TGGC), which significantly outperforms most existing models with only linear components and shows better model efficiency.

** 📦 This repository contains the code for the basic implementation of TGGC **

• numpy==1.23.3
• pandas==1.4.4
• torch==1.13.0

To install all dependencies:

pip install -r requirements.txt

Four traffic benchmarks are included under the path of ./dataset

Enter the directory with training scripts

cd scripts/

To train on the PeMS03 dastaset:

• bash pems03.sh
• Example output: ./output/pems03.log

To train on the PeMS04 dastaset:

• bash pems04.sh
• Example output: ./output/pems04.log

To train on the PeMS07 dastaset:

• bash pems07.sh
• Example output: ./output/pems07.log

To train on the PeMS08 dastaset:

• bash pems08.sh
• Example output: ./output/pems08.log

Please refer to the function get_args() in main.py for the description of each hyperparameter.

Our implementation adapts StemGNN and MTGODE as the code base and have extensively modified it to our purposes. We thank the authors for sharing their implementations and related resources.