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SUMMARY:Covariance-Modulated Optimal Transport Geometry
DTSTART:20230711T120000Z
DTEND:20230711T130000Z
DTSTAMP:20260505T004700Z
UID:indico-event-10047@indico.math.cnrs.fr
DESCRIPTION:Speakers: Franca Hoffmann (CalTech)\n\nWe present a variant of
  the dynamical optimal transport problem in which the energy to be minimis
 ed is modulated by the covariance matrix of the current distribution. Such
  transport metrics arise naturally in mean-field limits of certain ensembl
 e Kalman methods for solving inverse problems. We show that the transport 
 problem splits into two coupled minimization problems up to degrees of fre
 edom given by rotations: one for the evolution of mean and covariance of t
 he interpolating curve\, and one for its shape. Similarly\, on the level o
 f the gradient flows a similar splitting into the evolution of moments and
  shapes of the distribution can be observed. Those show better convergence
  properties in comparison to the classical Wasserstein metric in terms of 
 exponential convergence rates independent of the Gaussian target.\n\nhttps
 ://indico.math.cnrs.fr/event/10047/
LOCATION:Fokko du Cloux (Bâtiment Braconnier\, La Doua)
URL:https://indico.math.cnrs.fr/event/10047/
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