The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

E. Weinan, Bing Yu

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

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.

Original languageEnglish (US)
JournalCommunications in Mathematics and Statistics
Volume6
Issue number1
DOIs
StatePublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics
  • Statistics and Probability

Keywords

  • Deep Ritz Method
  • Eigenvalue problems
  • PDE
  • Variational problems

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