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CATEGORIES:Applied and Computational Analysis
SUMMARY:Wasserstein Hamiltonian flow and its structure pre
 serving numerical scheme - Jianbo Cui (The Hong Ko
 ng Polytechnic University)
DTSTART;TZID=Europe/London:20250626T150000
DTEND;TZID=Europe/London:20250626T160000
UID:TALK229717AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/229717
DESCRIPTION:We study discretizations of Hamiltonian systems on
  the probability density manifold equipped with th
 e L2-Wasserstein metric. For low dimensional probl
 ems\, based on discrete optimal transport theory\,
  several Wasserstein Hamiltonian flows (WHFs) on g
 raph are derived. They can be viewed as spatial di
 scretizations to the original systems. By regulari
 zing the system using Fisher information\, we prop
 ose a novel regularized symplectic scheme which co
 uld preserve several desirable longtime behaviors.
  Furthermore\, we use the coupling idea and WHF to
  propose a supervised learning scheme for some hig
 h-dimensional problem. If time permits we will tal
 k about more details on solving high-dimensional H
 amilton-Jacobi equation via the density coupling a
 nd supervised learning.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Georg Maierhofer
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