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SUMMARY:Optimal Transport and Gradient Flows: A Discrete-to-Continuum Appr
 oximation Problem
DTSTART:20191218T151500
DTEND:20191218T160000
DTSTAMP:20260415T010929Z
UID:a05a01e67b90d5365a15365a5c826dab07d77bf405b0a26da7ae60e1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Lorenzo PORTINALE (IST\, Autriche)\nAbstract:\nIn the se
 minal work of Jordan\, Kinderlehrer and Otto (’98) the authors showed th
 at the heat flow on R^d can be seen as gradient flow of the relative entro
 py functional in the space of probability measures with respect to the Was
 serstein distance W2. The correspondent discrete counterpart is represente
 d by the work of Maas (2011) and Mielke (2011)\, where a new notion of dis
 crete dynamical optimal transport has been introduced and a similar result
  has been obtained. In this talk we first recall the classical gradient fl
 ow structure of the Fokker-Planck equation in R^d and the connection with 
 the optimal transport problem. Secondly\, we describe a classical finite v
 olume method-type discretization of the equation\, to which we are able to
  associate a natural graph structure\, together with the correspondent dis
 crete transport distance. We then analyze the correspondent discrete gradi
 ent flow structure and from that we discuss some convergence results\, bot
 h concerning the discrete transport costs and the evolutionary G-convergen
 ce of the discrete gradient flow structures to the one associated to the c
 ontinuous Fokker-Planck equation.\nThis project is based on joint works wi
 th Dominik Forkert\, Eva Kopfer\, Peter Gladbach and Jan Maas.\n 
LOCATION:MED 0 1418 https://plan.epfl.ch/?room==MED%200%201418
STATUS:CONFIRMED
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