We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonline...We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonlinear,naturally adaptive and has the potential to work in rather high dimensions.The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning.We illustrate the method on several problems including some eigenvalue problems.展开更多
基金supported in part by the National Key Basic Research Program of China 2015CB856000Major Program of NNSFC under Grant 91130005,DOE Grant DE-SC0009248ONR Grant N00014-13-1-0338.
文摘We propose a deep learning-based method,the Deep Ritz Method,for numerically solving variational problems,particularly the ones that arise from par-tial differential equations.The Deep Ritz Method is naturally nonlinear,naturally adaptive and has the potential to work in rather high dimensions.The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning.We illustrate the method on several problems including some eigenvalue problems.
