{"id":286,"date":"2026-09-14T10:09:16","date_gmt":"2026-09-14T08:09:16","guid":{"rendered":"https:\/\/project.inria.fr\/cfd60ai\/?page_id=286"},"modified":"2026-09-14T10:12:58","modified_gmt":"2026-09-14T08:12:58","slug":"dlombardi","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/cfd60ai\/dlombardi\/","title":{"rendered":""},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center\"><strong>Damiano Lombardi<\/strong><\/h2>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Inria Paris &#8211; \ud83c\uddeb\ud83c\uddf7 Paris (France)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\">Optimal transport and model reduction<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this talk we are going to recall the fundamentals of the Optimal Transport (OT) problem. In particular, we are going to highlight how the Wasserstein distance could be seen as a natural way to evaluate the distance between snapshots in phenomena dominated by transport and how the McCann interpolation provides a natural way to interpolate between them.<br>Moreover, we are going to discuss about how the set of snapshots, endowed with the Wasserstein distance, could appear as &#8216;less high-dimensional&#8217; than the same set of snapshots when we use, as metric, Sobolev norms such as <math data-latex=\"L^2\"><semantics><msup><mi>L<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">L^2<\/annotation><\/semantics><\/math> or <math data-latex=\"H^1\"><semantics><msup><mi>H<\/mi><mn>1<\/mn><\/msup><annotation encoding=\"application\/x-tex\">H^1<\/annotation><\/semantics><\/math>. An analytical exemple in this respect is discussed.<br>Several numerical examples are described, highlighting encouraging aspects and shortcomings of the use of OT in model reduction.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Damiano Lombardi Inria Paris &#8211; \ud83c\uddeb\ud83c\uddf7 Paris (France) Optimal transport and model reduction In this talk we are going to recall the fundamentals of the Optimal Transport (OT) problem. In particular, we are going to highlight how the Wasserstein distance could be seen as a natural way to evaluate the\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/cfd60ai\/dlombardi\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":2613,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_members_access_role":[],"_members_access_error":""},"class_list":["post-286","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/users\/2613"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/comments?post=286"}],"version-history":[{"count":2,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/286\/revisions"}],"predecessor-version":[{"id":289,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/286\/revisions\/289"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/media?parent=286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}