The back-and-forth method for Wasserstein gradient flows
نویسندگان
چکیده
We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on generalization of the back-and-forth (BFM) introduced in Jacobs and Léger [ Numer. Math. 146 (2020) 513–544.]. solve optimal transport problems. evolve flow by solving dual problem JKO scheme. In general, much better behaved than primal problem. This allows us run large scale flows simulations for class internal energies including singular non-convex energies.
منابع مشابه
Lattice Fokker-Planck Method Based on Wasserstein Gradient Flows
Abstract A lattice Fokker-Planck method is introduced based upon a variational formulation of the time evolution as a Wasserstein gradient flow within the space of probability densities of the system. Gradient descent directions are efficiently generated by exploiting the link to Langevin dynamics and the parallel-execution capabilities of graphics processing units. This approach can capture al...
متن کاملOn gradient structures for Markov chains and the passage to Wasserstein gradient flows
We study the approximation of Wasserstein gradient structures by their finitedimensional analog. We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible Markov chains. Then we reprove the convergence of the discrete scheme in the limit of vanishing mesh size using only the involved gr...
متن کاملGradient Flows on Wasserstein Spaces over Compact Alexandrov Spaces
We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below. By using this Riemannian structure, we formulate and construct gradient flows of functions on such spaces. If the underlying space is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the free energy produces a solution of the l...
متن کاملBack and forth bisimulations
This paper is concerned with bisimulation relations which do not only require related agents to simulate each others behavior in the direction of the arrows, but also to simulate each other when going back in history. First it is demonstrated that the back and forth variant of strong bisimulation leads to the same equivalence as the ordinary notion of strong bisimulation. Then it is shown that ...
متن کاملKramers’ formula for chemical reactions in the context of Wasserstein gradient flows
We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well potential. The convergence proof is based on the Rayleigh principle of the underlying Wasser-stein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2021
ISSN: ['1262-3377', '1292-8119']
DOI: https://doi.org/10.1051/cocv/2021029