{"id":2794,"date":"2021-06-03T10:30:55","date_gmt":"2021-06-03T15:30:55","guid":{"rendered":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/?post_type=tribe_events&#038;p=2794"},"modified":"2021-06-03T10:30:55","modified_gmt":"2021-06-03T15:30:55","slug":"virtual-lans-seminar-42","status":"publish","type":"tribe_events","link":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/event\/virtual-lans-seminar-42\/","title":{"rendered":"Virtual LANS Seminar"},"content":{"rendered":"<p><strong>Seminar Title<\/strong>: Solving PDEs With Gaussian Processes<br \/>\n<strong>Speaker<\/strong>: Andrew Stuart<br \/>\n<strong>Title<\/strong>: Bren Professor of Computing and Mathematical Sciences, Caltech<\/p>\n<p><strong>Date\/Time<\/strong>: June 9, 2021 \/ 10:30 AM &#8211; 11:30 AM<br \/>\n<strong>Location<\/strong>: See meeting URL on the cels-seminars website\u00a0(requires Argonne login)<\/p>\n<p><strong>Description<\/strong>: We describe an approach to solving PDEs in which the solution is found by minimizing a squared RKHS norm subject to a penalty, or constraint, defined via the PDE. This links to the subject of Gaussian processes subject to pointwise nonlinear constraints. We introduce a framework for the methodology, establish convergence of the resulting numerical method, and describe numerical results. Forward problems for a nonlinear elliptic PDE, Burgers&#8217; equation and a regularized Eikonal equation are presented; and the method is extended to inverse problems and applied to the problem of permeability identification in the Darcy model of flow in a porous medium.<\/p>\n<p>This is in collaboration with Yifan Chen, Bamdad Hosseini and Houman Owhadi.<\/p>\n<p><em>Please note that the meeting URL for this event can be seen on the <\/em>cels-seminars website<em>, which requires an Argonne login.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Seminar Title: Solving PDEs With Gaussian Processes Speaker: Andrew Stuart Title: Bren Professor of Computing and Mathematical Sciences, Caltech Date\/Time: June 9, 2021 \/ 10:30 AM &#8211; 11:30 AM Location: See meeting URL on the cels-seminars website\u00a0(requires Argonne login) Description: &hellip; <a href=\"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/event\/virtual-lans-seminar-42\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":43,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"tags":[],"tribe_events_cat":[2],"class_list":["post-2794","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-seminar","cat_seminar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/users\/43"}],"version-history":[{"count":1,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2794\/revisions"}],"predecessor-version":[{"id":2795,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2794\/revisions\/2795"}],"wp:attachment":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/media?parent=2794"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tags?post=2794"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events_cat?post=2794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}