  We propose a deep learning based method, the Deep Ritz Method, for
numerically solving variational problems, particularly the ones that arise from
partial 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.
