{"id":2498,"date":"2025-03-19T07:02:21","date_gmt":"2025-03-19T07:02:21","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/19\/2503-13791\/"},"modified":"2025-03-19T07:02:21","modified_gmt":"2025-03-19T07:02:21","slug":"2503-13791","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/19\/2503-13791\/","title":{"rendered":"ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces"},"content":{"rendered":"<p>    ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2503.13791v1 Announce Type: new<br \/>\nAbstract: We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging techniques. Finally we apply our formulation to generalize the multivariate occupation kernel (MOCK) method for learning dynamical systems from data proposing the more general Riesz Occupation Kernel (ROCK) method. Our generalized methods are both more computationally efficient and performant on most of the benchmarks we test against.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Victor Rielly, Kamel Lahouel, Chau Nguyen, Bruno Jedynak<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2503.13791\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces arXiv:2503.13791v1 Announce Type: new Abstract: We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[2057,1135,2058],"class_list":["post-2498","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-formulation","tag-kernel","tag-occupation"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2498"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=2498"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2498\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}