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,

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Understanding and mitigating gradient pathologies in physics-informed neural networks
• When and why PINNs fail to train: A neural tangent kernel perspective
• A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
• MultiAdam: Parameter-wise Scale-invariant Optimizer for Multiscale Training of Physics-informed Neural Networks
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
• Sobolev Training for Physics Informed Neural Networks
• Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
• hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations

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}
}