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
• PyTorch
• MATLAB (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][arXiv]
[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][arXiv]
[3] Y Liao, P Ming. Deep Nitsche method: Deep Ritz method with essential boundary conditions. 2019. [arXiv]