# DeepRitz

**Repository Path**: xlk159357/DeepRitz

## Basic Information

- **Project Name**: DeepRitz
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-05-14
- **Last Updated**: 2021-05-14

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# DeepRitz&DeepGalerkin

## Implementation of the Deep Ritz method and the Deep Galerkin method

Four problems are solved using the Deep Ritz method, see 2dpoisson-autograd.py, 2dpoisson-hole-autograd.py, 10dpoisson-cube-autograd.py, and 10dpoisson-autograd.py. Four problems are solved using least square functionals, see 2dpoisson-ls-autograd.py, 2dpoisson-hole-ls-autograd.py, 10dpoisson-cube-ls-autograd.py, and 10dpoisson-ls-autograd.py.

## Dependencies

* [NumPy](https://numpy.org)
* [PyTorch](https://pytorch.org/)
* [MATLAB](https://www.mathworks.com/products/matlab.html) (for post-processing only)

## References

[1] W E, B Yu. The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems. <em>Communications in Mathematics and Statistics</em> 2018, 6:1-12. [[journal]](https://link.springer.com/article/10.1007/s40304-018-0127-z)[[arXiv]](https://arxiv.org/abs/1710.00211)  
[2] J Sirignano, K Spiliopoulos. DGM: A deep learning algorithm for solving partial differential equations. <em>Journal of Computational Physics</em> 2018, 375:1339–1364. [[journal]](https://www.sciencedirect.com/science/article/pii/S0021999118305527)[[arXiv]](https://arxiv.org/abs/1708.07469)  
[3] Y Liao, P Ming. Deep Nitsche method: Deep Ritz method with essential boundary conditions. 2019. [[arXiv]](https://arxiv.org/abs/1912.01309)