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SUMMARY:Christian Lubich (University of Tübingen)
DTSTART:20240409T111500Z
DTEND:20240409T120000Z
DTSTAMP:20260417T003326Z
UID:cam/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/cam/32/">Reg
 ularized dynamical nonlinear parametric approximation</a>\nby Christian Lu
 bich (University of Tübingen) as part of CAM seminar\n\nLecture held in M
 V:L14.\n\nAbstract\nThis talk is about the numerical approximation of solu
 tions to initial value problems of high-dimensional ordinary differential 
 equations or evolutionary partial differential equations such as the Schr\
 \"odinger equation by nonlinear parametrizations $u(t)=\\Phi(q(t))$ with t
 ime-dependent parameters $q(t)$\, which are to be determined in the comput
 ation. Our motivation comes from approximations by multiple Gaussians in q
 uantum dynamics\, by tensor networks\, and by neural networks. In all thes
 e cases\, the parametrization is typically irregular: the derivative $\\Ph
 i'(q)$ can have arbitrarily small singular values and may have varying ran
 k. The talk is about approximation results for a regularized approach\, wh
 ich can still be successfully applied in such irregular situations\, even 
 if it runs counter to the basic principle in numerical analysis to avoid s
 olving ill-posed subproblems when aiming for a stable algorithm.\nThe talk
  is based on joint work with Jörg Nick\, Caroline Lasser and Michael Feis
 chl.\n
LOCATION:https://researchseminars.org/talk/cam/32/
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