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We propose a deep learning based method, the Deep Ritz Method, fornumerically solving variational problems, particularly the ones that arise frompartial differential equations. The Deep Ritz method is naturally nonlinear,naturally adaptive and has the potential to work in rather high dimensions. Theframework is quite simple and fits well with the stochastic gradient descentmethod used in deep learning. We illustrate the method on several problemsincluding some eigenvalue problems.

The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems