Titre :

From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows

Auteur(s) :

Gallouët, Thomas [Auteur]
Méthodes particulaires utilisant Monge-Ampère [PARMA]
Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales [MOKAPLAN]
Natale, Andrea [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Todeschi, Gabriele [Auteur]
Institut des Sciences de la Terre [ISTerre]

Titre de la revue :

Mathematics of Computation

Pagination :

2769-2810

Éditeur :

American Mathematical Society

Date de publication :

2024

ISSN :

0025-5718

Mot(s)-clé(s) en anglais :

Optimal transport
Wasserstein extrapolation
Wasserstein gradient flows
BDF2

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the notion of geodesic extrapolation in the ...
Lire la suite >We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the notion of geodesic extrapolation in the Wasserstein space, which in general is not uniquely defined. We propose several possible definitions for such an operation, and we prove convergence of the resulting scheme to the limit PDE, in the case of the Fokker-Planck equation. For a specific choice of extrapolation we also prove a more general result, that is convergence towards EVI flows. Finally, we propose a variational finite volume discretization of the scheme which numerically achieves second order accuracy in both space and time.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Monge-Ampère et Géométrie Algorithmique
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL