{"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/dynamic-mode-decomposition-and-koopman-theory","title":"Dynamic Mode Decomposition and Koopman Theory","arxiv_id":"2211.07561","date":"2022-11-14","proceeding":null,"authors":["Sourya Dey"],"abstract":"Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system into a new domain which facilitates linearization. This is a technical report on DMD and Koopman theory, with primary focus on explaining the underlying mathematics in clear and concise form. We include dimensions of vectors and marices, and step-by-step derivations of equations in order to assist the user in easily comprehending these concepts. This report will also enable users to implement DMD and Koopman theory in code.","url_abs":"https://arxiv.org/abs/2211.07561v1","url_pdf":"https://arxiv.org/pdf/2211.07561v1.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":"dynamic-mode-decomposition-and-koopman-theory","repo_url":"https://github.com/galoisinc/dlkoopman","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}