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SUMMARY:24 Novembre 2025\, Nicolas Masson et Borjan Geshkovski
DTSTART:20251124T110000Z
DTEND:20251124T130000Z
DTSTAMP:20260504T171000Z
UID:indico-event-14582@indico.math.cnrs.fr
DESCRIPTION:Nicolas Masson (Université Paris-Saclay)\n \nTitle : Modelin
 g « polite » crowds : asymptotics of weighted projection problems \n \
 nAbstract : In 2010\, Aude-Roudneff Chupin proposed in her PhD thesis a ne
 w macroscopic crowd motion model\, yielding an unclassified PDE that coupl
 es a continuity equation and a Hilbertian projection problem. Together wit
 h Bertrand Maury and Filippo Santambrogio\, they proved the existence of a
  solution to this new PDE system\, and enhanced the underlying gradient fl
 ow structure using a JKO scheme. However\, this model allowed individuals 
 to travel faster than their desired velocity - which contradicts several e
 mpirical laws in crowd motion. The aim of this talk will be to present rel
 ated optimization problems that were introduced to correct these modeling 
 issues\, and show how the study of these problems helps address the challe
 nge of modeling « polite » crowds.\n \n \nBorjan Geshkovski (LJLL\, IN
 RIA)\nTitle: Approximate conditional flow matching\n \nAbstract: In the c
 ontext of (normalizing) flow matching\, one parametrizes the vector field 
 of a continuity equation using a two-layer neural network and fits the par
 ameters to minimize a discrepancy between the resulting solution and an un
 known target measure. We focus on the conditional transport problem\, wher
 e the goal is also to approximate the transport map that pushes forward th
 e initial condition to the unknown target measure. We provide an explicit 
 construction of parameters that are piecewise constant in time\, enabling 
 the simultaneous approximation of both the measure (in total variation) vi
 a the continuity equation and the transport map (in L2) via the associated
  solution map. This construction has the desirable property that the resul
 ting solution map closely resembles the Knothe–Rosenblatt rearrangement 
 between suitable discretizations of the measures.\n\nhttps://indico.math.c
 nrs.fr/event/14582/
LOCATION:Salle Maryam Mirzakhani (201) (Institut Henri Poincaré)
URL:https://indico.math.cnrs.fr/event/14582/
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