Title :

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

Author(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]

Journal title :

Mathematics of Computation

Pages :

2769-2810

Publisher :

American Mathematical Society

Publication date :

2024

ISSN :

0025-5718

English keyword(s) :

Optimal transport
Wasserstein extrapolation
Wasserstein gradient flows
BDF2

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

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