{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-deep-ritz-method-a-deep-learning-based","title":"The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems","arxiv_id":"1710.00211","date":"2017-09-30","proceeding":null,"authors":["Weinan E","Bing Yu"],"abstract":"We propose a deep learning based method, the Deep Ritz Method, for\nnumerically solving variational problems, particularly the ones that arise from\npartial differential equations. The Deep Ritz method is naturally nonlinear,\nnaturally adaptive and has the potential to work in rather high dimensions. The\nframework is quite simple and fits well with the stochastic gradient descent\nmethod used in deep learning. We illustrate the method on several problems\nincluding some eigenvalue problems.","url_abs":"http://arxiv.org/abs/1710.00211v1","url_pdf":"http://arxiv.org/pdf/1710.00211v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-deep-ritz-method-a-deep-learning-based","repo_url":"https://github.com/junbinhuang/DeepRitz","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.00211","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}