Here is the official PyTorch implementation of the paper: Tackling the Curse of Dimensionality with Physics-Informed Neural Networks.
The paper is coauthored by Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi.
It has been accepted by Neural Networks.
arXiv version: https://arxiv.org/abs/2307.12306
Journal version (Open Access): https://www.sciencedirect.com/science/article/pii/S0893608024002934
If you think the code is useful, kindly cite our paper.
@article{hu2024tackling,
title={Tackling the curse of dimensionality with physics-informed neural networks},
author={Hu, Zheyuan and Shukla, Khemraj and Karniadakis, George Em and Kawaguchi, Kenji},
journal={Neural Networks},
pages={106369},
year={2024},
publisher={Elsevier}
}You may also consider citing our other papers on high-dimensional and high-order PINN and PDE, whose codes will also be publicly available once they are accepted.
@article{hu2024hutchinson,
title={Hutchinson trace estimation for high-dimensional and high-order physics-informed neural networks},
author={Hu, Zheyuan and Shi, Zekun and Karniadakis, George Em and Kawaguchi, Kenji},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={424},
pages={116883},
year={2024},
publisher={Elsevier}
}Code is available at https://github.com/zheyuanhu01/HTE_PINN.
@article{hu2023bias,
title={Bias-variance trade-off in physics-informed neural networks with randomized smoothing for high-dimensional PDEs},
author={Hu, Zheyuan and Yang, Zhouhao and Wang, Yezhen and Karniadakis, George Em and Kawaguchi, Kenji},
journal={arXiv preprint arXiv:2311.15283},
year={2023}
}@article{hu2024score,
title={Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations},
author={Hu, Zheyuan and Zhang, Zhongqiang and Karniadakis, George Em and Kawaguchi, Kenji},
journal={arXiv preprint arXiv:2402.07465},
year={2024}
}