HoGRC

Higher-order Granger reservoir computing

This repository contains the code for the paper:

• [Higher-order Granger reservoir computing: Simultaneously achieving structures inference and accurate prediction of complex dynamics]

In this work, we formulate a new dynamic inference and prediction framework based on reservior computing and Granger causality. Our framework can not only accurately infer the higher-order structures of the system, but also significantly outperforms the baseline methods in prediction tasks.

This respository provides HoGRC methods implemented in PyTorch. And the experimental data can be generated through code.

Environment

To run this project, we will need to set up an environment with Python 3 and install the following Python packages:

• Python 3.9.7
• joblib 1.3.2
• matplotlib 3.8.2
• numpy 1.26.2
• pandas 2.1.4
• scipy 1.11.4
• scikit-learn 1.3.2
• torch 2.1.2
• torchdiffeq 0.2.3

pip install -r requirements.txt

Examples

• 'An_Example_for_Task_1.py' serves as an example for inferring the high-order neighbors of node z in the Loren63 system, and the results are displayed in Fig. 2a in the main text.

python -m An_Example_for_Task_1

• 'An_Example_for_Task_2.py' serves as an example for prediction of the coupled FitzHugh-Nagumo system using different methods, and the results are displayed in Figs. 3a and 3c in the main text.

python -m An_Example_for_Task_2

• 'Automatic_Example_for_Task_1.py' combines the Algorithm 1 of the main text to implement automatic structural inference. It is an automated inference version of the "An_Example_for_Task_1.py" task.

python -m Automatic_Example_for_Task_1

Here, we illustrate the structure inference process of the HoGRC framework in a simple case using a GIF:

It should be noted that the input information for the HoGRC framework is not limited to polynomial forms. It can comprise arbitrary nonlinear functions or interactions that cannot be represented by elementary functions. As the inputs are structural information (represented by simplicial complexes), the exact type of the interaction dynamics is learned through RC.

Files

• 'main_L63.py' is HoGRC experiment for the Lorenz63 system, including five parts: hyperparameter setting , data generation, the configuration of higher-order structures, model training and testing.
• 'main_CL63.py' is HoGRC experiment for the coupled Lorenz system.
• 'main_rossler.py' is HoGRC experiment for the Rossler system.
• 'main_CRo.py' is HoGRC experiment for the coupled Rossler system.
• 'main_FHN.py' is HoGRC experiment for the coupled FitzHugh-Nagumo system.
• 'main_HR.py' is HoGRC experiment for the coupled simplified Hodgkin–Huxley system.
• 'main_L96.py' is HoGRC experiment for the Lorenz96 system.
• 'main_NFW.py' is HoGRC experiment for the New Four Wings system.
• 'main_colpitts' is HoGRC experiment for the Colpitts system.

Please refer to the code comments and the "workflow.md" file for detailed execution specifics of these experiments.

File folders

• 'power_grid' folder contains the experiments for higher-order Kuramoto dynamics on the UK power grid.
• 'models' folder: used to store model files
• 'dataset' folder: used to store dataset files
• 'results' folder: used to store results files

Citing

If you use HoGRC in an academic paper, please cite:

@article{li2024higher,
  title={Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction},
  author={Li, Xin and Zhu, Qunxi and Zhao, Chengli and Duan, Xiaojun and Zhao, Bolin and Zhang, Xue and Ma, Huanfei and Sun, Jie and Lin, Wei},
  journal={Nature Communications},
  volume={15},
  number={1},
  pages={2506},
  year={2024},
  publisher={Nature Publishing Group UK London}
}