MTGODE

This is the official PyTorch implementation of the paper "Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs", accepted to IEEE Transactions on Knowledge and Data Engineering (TKDE), 2022.

Dependencies

numpy==1.19.2
scipy==1.5.4
torch==1.7.1
torchdiffeq==0.2.3

To install all dependencies:

pip install -r requirements.txt

Download datasets

• You can download the datasets from here.

• Please put all dataset files under the ./data directory.

Reproducibility

Here we provide two examples (i.e., METR-LA and Electricity)

In terminal

• Option 1. Run the shell scripts (i.e., eleltricity.sh and metr-la.sh)

cd run
bash metr-la.sh

• Option 2. Run the python files
  • To run on METR-LA:

  python run_multi_step.py --data ./data/METR-LA --buildA_true True --expid 0 --runs 1 --device cuda:0 --save_preds False --num_nodes 207 --epochs 200 --batch_size 64 --learning_rate 0.001 --weight_decay 0.0001 --lr_decay True --lr_decay_steps 100 --lr_decay_rate 0.1 --dropout 0.3 --node_dim 40 --subgraph_size 20 --num_split 1 --tanhalpha 3 --conv_channels 64 --end_channels 128 --solver_1 euler --time_1 1.0 --step_1 0.25 --solver_2 euler --time_2 1.0 --step_2 0.25 --alpha 2.0 --rtol 1e-4 --atol 1e-3 --adjoint False --perturb False
  

  • To run on Electricity (horizon=3):

  python run_single_step.py --data ./data/electricity.txt --expid 0 --runs 1 --device cuda:0 --save_preds False --num_nodes 321 --horizon 3 --epochs 60 --batch_size 4 --lr 0.001 --weight_decay 0.0001 --lr_decay True --lr_decay_steps '20,40' --lr_decay_rate 0.5 --dropout 0.3 --node_dim 40 --subgraph_size 20 --num_split 1 --tanhalpha 3 --conv_channels 64 --end_channels 64 --solver_1 euler --time_1 1.0 --step_1 0.2 --solver_2 euler --time_2 1.0 --step_2 0.5 --alpha 1.0 --rtol 1e-4 --atol 1e-3 --adjoint False --perturb False
  

Results

Here we provide the results of the above two examples

• METR-LA

Training finished
The valid loss on best model is 2.6909
Evaluate best model on test data for horizon 1, Test MAE: 2.2302, Test MAPE: 0.0539, Test RMSE: 3.8937
Evaluate best model on test data for horizon 2, Test MAE: 2.4785, Test MAPE: 0.0620, Test RMSE: 4.6105
Evaluate best model on test data for horizon 3, Test MAE: 2.6491, Test MAPE: 0.0682, Test RMSE: 5.0816
Evaluate best model on test data for horizon 4, Test MAE: 2.7805, Test MAPE: 0.0732, Test RMSE: 5.4578
Evaluate best model on test data for horizon 5, Test MAE: 2.8886, Test MAPE: 0.0775, Test RMSE: 5.7657
Evaluate best model on test data for horizon 6, Test MAE: 2.9818, Test MAPE: 0.0812, Test RMSE: 6.0234
Evaluate best model on test data for horizon 7, Test MAE: 3.0659, Test MAPE: 0.0845, Test RMSE: 6.2481
Evaluate best model on test data for horizon 8, Test MAE: 3.1410, Test MAPE: 0.0873, Test RMSE: 6.4417
Evaluate best model on test data for horizon 9, Test MAE: 3.2070, Test MAPE: 0.0899, Test RMSE: 6.6087
Evaluate best model on test data for horizon 10, Test MAE: 3.2681, Test MAPE: 0.0924, Test RMSE: 6.7568
Evaluate best model on test data for horizon 11, Test MAE: 3.3243, Test MAPE: 0.0946, Test RMSE: 6.8920
Evaluate best model on test data for horizon 12, Test MAE: 3.3835, Test MAPE: 0.0968, Test RMSE: 7.0258

• Electricity (horizon=3)

final test rse 0.0728 | test rae 0.0415 | test corr 0.9431

Cite us

If you use this code in your research, please cite the following article:

@article{jin2022multivariate,
  title={Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs},
  author={Jin, Ming and Zheng, Yu and Li, Yuan-Fang and Chen, Siheng and Yang, Bin and Pan, Shirui},
  journal={IEEE Transactions on Knowledge and Data Engineering (TKDE)},
  year={2022}
}

Acknowledgement

Our implementation adapts the code here as the code base and extensively adapts it to our purpose. We thank the authors for sharing their code.