{"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/data-driven-discovery-of-closure-models","title":"Data-driven Discovery of Closure Models","arxiv_id":"1803.09318","date":"2018-03-25","proceeding":null,"authors":["Shaowu Pan","Karthik Duraisamy"],"abstract":"Derivation of reduced order representations of dynamical systems requires the\nmodeling of the truncated dynamics on the retained dynamics. In its most\ngeneral form, this so-called closure model has to account for memory effects.\nIn this work, we present a framework of operator inference to extract the\ngoverning dynamics of closure from data in a compact, non-Markovian form. We\nemploy sparse polynomial regression and artificial neural networks to extract\nthe underlying operator. For a special class of non-linear systems,\nobservability of the closure in terms of the resolved dynamics is analyzed and\ntheoretical results are presented on the compactness of the memory. The\nproposed framework is evaluated on examples consisting of linear to nonlinear\nsystems with and without chaotic dynamics, with an emphasis on predictive\nperformance on unseen data.","url_abs":"http://arxiv.org/abs/1803.09318v3","url_pdf":"http://arxiv.org/pdf/1803.09318v3.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":"data-driven-discovery-of-closure-models","repo_url":"https://github.com/pswpswpsw/siads_data_driven_closure","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"form","task_name":"Form"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}