{"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/sparse-learning-of-stochastic-dynamic","title":"Sparse learning of stochastic dynamic equations","arxiv_id":"1712.02432","date":"2017-12-06","proceeding":null,"authors":["Lorenzo Boninsegna","Feliks Nüske","Cecilia Clementi"],"abstract":"With the rapid increase of available data for complex systems, there is great\ninterest in the extraction of physically relevant information from massive\ndatasets. Recently, a framework called Sparse Identification of Nonlinear\nDynamics (SINDy) has been introduced to identify the governing equations of\ndynamical systems from simulation data. In this study, we extend SINDy to\nstochastic dynamical systems, which are frequently used to model biophysical\nprocesses. We prove the asymptotic correctness of stochastics SINDy in the\ninfinite data limit, both in the original and projected variables. We discuss\nalgorithms to solve the sparse regression problem arising from the practical\nimplementation of SINDy, and show that cross validation is an essential tool to\ndetermine the right level of sparsity. We demonstrate the proposed methodology\non two test systems, namely, the diffusion in a one-dimensional potential, and\nthe projected dynamics of a two-dimensional diffusion process.","url_abs":"http://arxiv.org/abs/1712.02432v1","url_pdf":"http://arxiv.org/pdf/1712.02432v1.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":"sparse-learning-of-stochastic-dynamic","repo_url":"https://github.com/dynamicslab/langevin-regression","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"sparse-learning","task_name":"Sparse Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/denoising-on-darmstadt-noise-dataset","task":"Denoising","dataset":"Darmstadt Noise Dataset","model":"SINDy","rank_in_archive_order":1,"of":10,"metrics":{"PSNR":"81"},"uses_additional_data":false},{"leaderboard":"/sota/sparse-learning-on-imagenet","task":"Sparse Learning","dataset":"ImageNet","model":"SINDy","rank_in_archive_order":9,"of":9,"metrics":{"Top-1 Accuracy":"6"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1712.02432","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1712.02432"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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