{"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/machine-learning-and-finite-element-method","title":"Machine Learning and Finite Element Method for Physical Systems Modeling","arxiv_id":"1801.07337","date":"2018-01-22","proceeding":null,"authors":["O. Kononenko","I. Kononenko"],"abstract":"Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the problem size becomes large, time needed to solve the resulting linear systems may range from hours to weeks, and if the input parameters need to be adjusted, even slightly, the simulations has to be re-done from scratch. Recent advances in machine learning algorithms and their successful applications in various fields demonstrate that, if properly chosen and trained, these models can significantly improve conventional techniques. In this note we discuss possibilities to complement the finite element studies with machine learning and provide several basic examples.","url_abs":"http://arxiv.org/abs/1801.07337v2","url_pdf":"http://arxiv.org/pdf/1801.07337v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"machine-learning-and-finite-element-method","repo_url":"https://github.com/oleksiyskononenko/mlfem","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}