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SUMMARY:Wasserstein Hamiltonian flow and its structure preserving numerica
 l scheme - Jianbo Cui (The Hong Kong Polytechnic University)
DTSTART:20250626T140000Z
DTEND:20250626T150000Z
UID:TALK229717@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:We study discretizations of Hamiltonian systems on the probabi
 lity density manifold equipped with the L2-Wasserstein metric. For low dim
 ensional problems\, based on discrete optimal transport theory\, several W
 asserstein Hamiltonian flows (WHFs) on graph are derived. They can be view
 ed as spatial discretizations to the original systems. By regularizing the
  system using Fisher information\, we propose a novel regularized symplect
 ic scheme which could preserve several desirable longtime behaviors. Furth
 ermore\, we use the coupling idea and WHF to propose a supervised learning
  scheme for some high-dimensional problem. If time permits we will talk ab
 out more details on solving high-dimensional Hamilton-Jacobi equation via 
 the density coupling and supervised learning.
LOCATION:Centre for Mathematical Sciences\, MR14
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