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 accepted to NeurIPS 2024! 🎉

<p align="center"> <img width="80%" src="https://raw.githubusercontent.com/i207M/PINNacle/master/resources/pinnacle.png"/> </p>

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

# conda create -n pinnacle python=3.9
# conda activate pinnacle  # To keep Python environments separate
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}
}