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DTSTART;TZID=Europe/Paris:20251211T140000
DTEND;TZID=Europe/Paris:20251211T150000
DTSTAMP:20260409T061826
CREATED:20251118T085344Z
LAST-MODIFIED:20251212T144211Z
UID:14561-1765461600-1765465200@lmv.math.cnrs.fr
SUMMARY:EDP : Antonin Chambolle (université Paris Dauphine) : Analyse d'approximations du mouvement par courbure moyenne basées sur des réseaux de neurone
DESCRIPTION:Dans une série de travaux récents\, (Bretin et al) ont proposé plusieurs approches basées sur des réseaux de neurones pour « apprendre » et reproduire des flots géométriques (mouvement par courbure moyenne\, mouvement d’interfaces non-orientées\, flot de type Willmore…)\nDans cet exposé\, on s’intéressera au flot le plus élémentaire\, le mouvement par courbure moyenne des bords d’ensembles\, et on analysera la consistance de deux schémas numériques très simples\, qui expliquent (partiellement) pourquoi l’approximation par réseaux de neurones est si facile à mettre en œuvre dans ce cadre.
URL:https://lmv.math.cnrs.fr/evenenement/edp-antonin-chambolle-universite-paris-dauphine/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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DTSTART;TZID=Europe/Paris:20251211T153000
DTEND;TZID=Europe/Paris:20251211T163000
DTSTAMP:20260409T061826
CREATED:20251118T085457Z
LAST-MODIFIED:20251212T144225Z
UID:14563-1765467000-1765470600@lmv.math.cnrs.fr
SUMMARY:EDP : Sonia Fliss (ENSTA) : Wave propagation in quasi-periodic media
DESCRIPTION:This work\, done in collaboration with Pierre Amenoagbadji (Columbia University) and Patrick Joly (POEMS)\, is devoted to the solution of the Helmholtz equation in 1D unbounded quasiperiodic media. By this we mean that the coefficients appearing in the model are quasiperiodic functions of the 1D space variable\, namely the trace along a line of a periodic function of n variables. \nWhen the coefficients are periodic (which is a special case)\, several methods have been proposed to characterize and compute the solution. However\, when the coefficients are quasi-periodic without being periodic\, the above methods cannot be applied directly. \nWe use an original method\, that we call the lifting method\, which has been used in several papers on homogenization theory. The original problem can thus be lifted to an nD « augmented » problem with periodic coefficients\, and the 1D solution is the trace along this line of the nD solution. The advantage is that the periodicity of the augmented problem enables to use the ideas proposed for solving periodic Helmholtz equations in periodic waveguides. However\, since the augmented equation is a degenerate elliptic equation\, the corresponding tools have to be adapted since new difficulties arise both in the analysis and in the design of the resulting numerical method. \nI will present our results for the Helmholtz equation with dissipation (where the solution decays at infinity) and then for the equation without dissipation (where the solution can propagate to infinity)\, analyzing the latter case using a limiting absorption principle.
URL:https://lmv.math.cnrs.fr/evenenement/edp-sonia-fliss-ensta/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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