{"id":2683,"date":"2026-09-02T13:09:24","date_gmt":"2026-09-02T04:09:24","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/sdyang\/?p=2683"},"modified":"2026-09-02T13:10:34","modified_gmt":"2026-09-02T04:10:34","slug":"%ea%b0%95%ec%97%b0-2","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/sdyang\/%ea%b0%95%ec%97%b0-2\/","title":{"rendered":"\uac15\uc5f0"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>\uc5f0\uc0ac<\/strong>: \uc9c0\uc815\ubbfc \uad50\uc218 <br><strong>\uc18c\uc18d<\/strong>: Department of Mathematics, University of Louisville, USA<br><strong>\uc2dc\uac04<\/strong> : 2026\ub144 9\uc6d4 22\uc77c (\ud654) 4:30~5:30<br><strong>\uc7a5\uc18c<\/strong>: \uc544\uc0b0\uc774\ud559\uad00 524\ud638<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title<\/strong>: Analysis Informed Neural Network Methods for Singularly Perturbed Problems<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract<\/strong>: Singularly perturbed differential equations arise in many problems in fluid mechanics and related areas, where small diffusivity or viscosity can generate sharp boundary, interior, and corner layers. These multiscale structures present significant challenges for both classical numerical methods and standard neural network approaches.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We develop neural network methods that use asymptotic analysis to identify and incorporate the dominant structure of singular layers directly into the approximation. By explicitly incorporating the leading singular components into the neural network ansatz, the trainable component is used primarily to approximate the smoother part of the solution. We also consider conservative formulations based on finite volume residuals, which incorporate local flux balance into the learning framework. Numerical examples for a range of singularly perturbed problems demonstrate the accuracy and robustness of these approaches as the perturbation parameter tends to zero.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc5f0\uc0ac: \uc9c0\uc815\ubbfc \uad50\uc218 \uc18c\uc18d: Department of Mathematics, University of Louisville, USA\uc2dc\uac04 : 2026\ub144 9\uc6d4 22\uc77c (\ud654) 4:30~5:30\uc7a5\uc18c: \uc544\uc0b0\uc774\ud559\uad00 524\ud638 Title: Analysis Informed Neural Network Methods for Singularly Perturbed Problems Abstract: Singularly perturbed differential equations arise in many problems in fluid mechanics and related areas, where small diffusivity or viscosity can generate sharp boundary, interior, and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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