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Codebase for PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs.

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PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs

This repository is our codebase for PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs. Our paper is currently under review. We will provide more detailed guide soon.

Implemented Methods

This benchmark paper implements the following variants and create a new challenging dataset to compare them,

Method Type
PINN Vanilla PINNs
PINNs(Adam+L-BFGS) Vanilla PINNs
PINN-LRA Loss reweighting
PINN-NTK Loss reweighting
RAR Collocation points resampling
MultiAdam New optimizer
gPINN New loss functions (regularization terms)
hp-VPINN New loss functions (variational formulation)
LAAF New architecture (activation)
GAAF New architecture (activation)
FBPINN New architecture (domain decomposition)

See these references for more details,

Installation

git clone https://github.com/i207M/PINNacle.git --depth 1
cd PINNacle
pip install -r requirements.txt

Usage

📄 Full Documention

Run all 20 cases with default settings:

python benchmark.py [--name EXP_NAME] [--seed SEED] [--device DEVICE]

Citation

If you find out work useful, please cite our paper at:

@article{hao2023pinnacle,
  title={PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs},
  author={Hao, Zhongkai and Yao, Jiachen and Su, Chang and Su, Hang and Wang, Ziao and Lu, Fanzhi and Xia, Zeyu and Zhang, Yichi and Liu, Songming and Lu, Lu and others},
  journal={arXiv preprint arXiv:2306.08827},
  year={2023}
}

We also suggest you have a look at the survey paper (Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications) about PINNs, neural operators, and other paradigms of PIML.

@article{hao2022physics,
  title={Physics-informed machine learning: A survey on problems, methods and applications},
  author={Hao, Zhongkai and Liu, Songming and Zhang, Yichi and Ying, Chengyang and Feng, Yao and Su, Hang and Zhu, Jun},
  journal={arXiv preprint arXiv:2211.08064},
  year={2022}
}

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Codebase for PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs.

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