Finite-expression-method

By Senwei Liang and Haizhao Yang

This repo is the implementation of "Finite Expression Method for Solving High-Dimensional Partial Differential Equations" [paper].

Introduction

Finite expression method (FEX) is a new methodology that seeks an approximate PDE solution in the space of functions with finitely many analytic expressions. This repo provides a deep reinforcement learning method to implement FEX for various high-dimensional PDEs in different dimensions.

Environment

• PyTorch 1.0

Code structure

Finite-expression-method
│   README.md    <-- You are here
│
└─── fex    ----> three numerical examples with FEX
│   │   Poisson
│   │   Schrodinger
│   │   Conservationlaw
│   
└─── nn     ----> three numerical examples with NN
    │   Poisson
    │   Schrodinger
    │   Conservationlaw

Citing FEX

If you find our code is helpful for your research, please kindly cite

@article{liang2022finite,
  title={Finite Expression Method for Solving High-Dimensional Partial Differential Equations},
  author={Liang, Senwei and Yang, Haizhao},
  journal={arXiv preprint arXiv:2206.10121},
  year={2022}
}

Acknowledgments

We appreciate bearpaw for his DL framework and Taehoon Kim for his RL fromework.