Pytorch Implementation of Physics-informed-Neural-Networks(PINNs)

PINNs were designed to solve a partial differential equation(PDE) by Raissi et al.
The loss of PINNs is defined as PDE loss at collocation points and initial condition(IC) loss, boundary condition(BC) loss. I recommend you to read this for more details.

Getting Started

Prerequisites

This code has been tested with Pytorch 1.10.0, CUDA 11.5, Window 10. However, it would be fine with lower versions as well. The library versions used are:

numpy 1.21.2
scipy 1.7.2
matplotlib 3.4.3
pyDOE 0.3.8
pytorch 1.10.0

Installing

Install required packages:

pip install numpy==1.21.2 scipy==1.7.2 matplotlib==3.4.3 pydoe==0.3.8  
pip3 install torch==1.10.0+cu113 torchvision==0.11.1+cu113 torchaudio===0.10.0+cu113 -f https://download.pytorch.org/whl/cu113/torch_stable.html

Running

Run the main.py to train PINN, then run plot.py to generate result.

Result

Bergers-inference

Bergers-Identification

Heat Equation

Navier-Stokes Equation

Schrodinger Equation

1D Wave Equation

2D Wave Equation

License

This project is licensed under the MIT License - see the LICENSE

References

• Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations." arXiv preprint arXiv:1711.10561 (2017).

• Raissi, Maziar, Paris Perdikaris, and George Em Karniadakis. "Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations." arXiv preprint arXiv:1711.10566 (2017).

• Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Journal of Computational Physics 378 (2019): 686-707.

• Rao, C. P., H. Sun, and Y. Liu. "Physics-Informed Deep Learning for Incompressible Laminar Flows." Theoretical and Applied Mechanics Letters 10.3 (2020): 207-12.

• "비압축성 유체 정보 기반 신경망 (Incompressible NS-Informed Neural Network)", Deep Campus, 2021.11.02, https://pasus.tistory.com/166 (*Written in Korean)