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X-WR-CALDESC:Events for Biomedical Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20240101T000000
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DTSTART;TZID=Asia/Seoul:20250613T093000
DTEND;TZID=Asia/Seoul:20250613T110000
DTSTAMP:20260423T081156
CREATED:20250609T002038Z
LAST-MODIFIED:20250609T033628Z
UID:11164-1749807000-1749812400@www.ibs.re.kr
SUMMARY:Deep learning for universal linear embeddings of nonlinear dynamics - Hyukpyo Hong
DESCRIPTION:In this talk\, we discuss the paper “Deep learning for universal linear embeddings of nonlinear dynamics” by B. Lusch\, J. N. Kutz\, and S. Brunton\, Nat. Comm. 2018. \nAbstract  \nIdentifying coordinate transformations that make strongly nonlinear dynamics approximately linear has the potential to enable nonlinear prediction\, estimation\, and control using linear theory. The Koopman operator is a leading data-driven embedding\, and its eigenfunctions provide intrinsic coordinates that globally linearize the dynamics. However\, identifying and representing these eigenfunctions has proven challenging. This work leverages deep learning to discover representations of Koopman eigenfunctions from data. Our network is parsimonious and interpretable by construction\, embedding the dynamics on a low-dimensional manifold. We identify nonlinear coordinates on which the dynamics are globally linear using a modified auto-encoder. We also generalize Koopman representations to include a ubiquitous class of systems with continuous spectra. Our framework parametrizes the continuous frequency using an auxiliary network\, enabling a compact and efficient embedding\, while connecting our models to decades of asymptotics. Thus\, we benefit from the power of deep learning\, while retaining the physical interpretability of Koopman embeddings.
URL:https://www.ibs.re.kr/bimag/event/hyukpyo-hong/
LOCATION:B232 Seminar Room\, IBS\, 55 Expo-ro Yuseong-gu\, Daejeon\, Daejeon\, 34126\, Korea\, Republic of
CATEGORIES:Journal Club
ORGANIZER;CN="Jae Kyoung Kim":MAILTO:jaekkim@kaist.ac.kr
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