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SUMMARY:The JKO scheme based on Sinkhorn divergences
DTSTART:20261104T090000Z
DTEND:20261104T110000Z
DTSTAMP:20261104T143600Z
UID:indico-event-17642@indico.math.cnrs.fr
DESCRIPTION:Speakers: Aymeric Baradat\n\nWhen computing numerically soluti
 ons of Wasserstein gradient flows through the JKO scheme\, it can be usefu
 l to use an entropic version of the classical optimal transport problem in
  order to fasten the computations. However\, a drawback of this method is 
 that the entropic cost between two measures a and b is not minimal for a =
  b. Therefore\, this implies an additional dynamic\, and for instance\, th
 e sequence produced by the scheme does not converge towards the minimizer 
 of the energy functional of study. A way to solve this issue is to use the
  Sinkhorn divergence\, obtained by removing to the entropic optimal transp
 ort cost S(a\,b) the quantity (S(a\,a) + S(b\,b))/2\, so that the resultin
 g cost cancels when a = b. In this talk\, I will show that this version of
  the entropic JKO scheme in the case of a linear energy functional recover
 s the convergence towards minimizers\, I will describe formally the limiti
 ng curve obtained when the timestep goes to 0\, and I will prove convergen
 ce in the case of a finite base space. The talk is based on a paper by Har
 dion and Lavenant.\n\nhttps://indico.math.cnrs.fr/event/17642/
LOCATION:112 TBC (Braconnier )
URL:https://indico.math.cnrs.fr/event/17642/
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