{"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/structured-model-selection-via-ell-1-ell-2","title":"Structured model selection via $\\ell_1-\\ell_2$ optimization","arxiv_id":"2305.17467","date":"2023-05-27","proceeding":null,"authors":["Xiaofan Lu","Linan Zhang","Hongjin He"],"abstract":"Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is performed by a sparse least-squares fitting over a large set of candidate functions via a nonconvex $\\ell_1-\\ell_2$ sparse optimization solved by the alternating direction method of multipliers. Using a Bernstein-like inequality with a coherence condition, we show that if the set of candidate functions forms a structured random sampling matrix of a bounded orthogonal system, the recovery is stable and the error is bounded. The learning approach is validated on synthetic data generated by the viscous Burgers' equation and two reaction-diffusion equations. The computational results demonstrate the theoretical guarantees of success and the efficiency with respect to the ambient dimension and the number of candidate functions.","url_abs":"https://arxiv.org/abs/2305.17467v2","url_pdf":"https://arxiv.org/pdf/2305.17467v2.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":"structured-model-selection-via-ell-1-ell-2","repo_url":"https://github.com/linanzhang/nonconvexsparsecyclicrecovery","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"model","task_name":"model"}],"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}