{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:55:52Z","timestamp":1760151352702,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T00:00:00Z","timestamp":1646870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, and the dimension of the approximation space is systematically determined by a probability threshold. This random sampling procedure avoids large candidate sample sets for high-dimensional parameters, and the probability based stopping criterion can efficiently control the dimension of the approximation space. Numerical experiments are conducted to demonstrate the computational efficiency of SDEIM, which include separation of variables for general nonlinear functions, e.g., exponential functions of the Karhu nen\u2013Lo\u00e8ve (KL) expansion, and constructing reduced order models for FitzHugh\u2013Nagumo equations, where symmetry among limit cycles is well captured by SDEIM.<\/jats:p>","DOI":"10.3390\/sym14030556","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T20:19:10Z","timestamp":1646943550000},"page":"556","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Stochastic Discrete Empirical Interpolation Approach for Parameterized Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0756-1866","authenticated-orcid":false,"given":"Daheng","family":"Cai","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]},{"given":"Chengbin","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Natural Resources and Environment, Northwest A&F University, Xianyang 712100, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2033-6356","authenticated-orcid":false,"given":"Qifeng","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1137\/130932715","article-title":"A survey of projection-based model reduction methods for parametric dynamical systems","volume":"57","author":"Benner","year":"2015","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.crma.2004.08.006","article-title":"An \u2018empirical interpolation\u2019 method: Application to efficient reduced-basis discretization of partial differential equations","volume":"339","author":"Barrault","year":"2004","journal-title":"C. 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