{Euclidean, metric, and Wasserstein} gradient flows: an overview

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Gradient 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 کامل

An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows

We formulate quasistatic nonlinear finite-strain viscoelasticity of rate type as a gradient system. Our focus is on nonlinear dissipation functionals and distances that are related to metrics on weak diffeomorphisms and that ensure time-dependent frame indifference of the viscoelastic stress. In the multidimensional case we discuss which dissipation distances allow for the solution of the timei...

متن کامل

Gradient flows in asymmetric metric spaces

This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower semicontinuous in the second argu...

متن کامل

On 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 کامل

ذخیره 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: Bulletin of Mathematical Sciences

سال: 2017

ISSN: 1664-3607,1664-3615

DOI: 10.1007/s13373-017-0101-1