Related papers: Wasserstein Hamiltonian flow with common noise on …
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
This paper deals with the large-scale behaviour of nonlinear minimum-cost flow problems on random graphs. In such problems, a random nonlinear cost functional is minimised among all flows (discrete vector-fields) with a prescribed net flux…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…
We complement a recent work on the stability of fixed points of the CMC-Einstein-$\Lambda$ flow. In particular, we modify the utilized gauge for the Einstein equations and remove a restriction on the fixed points whose stability we are able…
This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…
The empirical measure flow of a McKean-Vlasov $n$-particle system with common noise is a measure-valued process whose law solves an associated martingale problem. We obtain a stability result for the sequence of martingale problems: all…
We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…
It has been shown that a global minimizer of a smooth determinant of a matrix function corresponds to the largest cycle of a graph. When it exists, this is a Hamiltonian cycle. Finding global minimizers even of a smooth function is a…
In this article, we formulate topology optimization problems concerning the mass distribution as minimization problems for functionals on the Wasserstein space. We relax optimization problems regarding non-convex objective functions on the…
The defining equation $(\ast):\ \dot \omega\_t=-F'(\omega\_t),$ of a gradient flow is kinetic in essence. This article explores some dynamical (rather than kinetic) features of gradient flows (i) by embedding equation $(\ast)$ into the…
In this paper, we are interested in proving the existence and uniqueness of the local, local maximal, and global solutions of the equation projected on the Hilbert manifold. Furthermore, we show that, for any given initial data in the…
This work is the third part of a program initiated in arXiv:2111.13258, arXiv:2302.06571 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a unique coercive stable fixed point subject to general additive Markovian noise in the limit of small…
This paper is devoted to a viscosity solution theory of the stochastic Hamilton-Jacobi-Bellman equation in the Wasserstein spaces for the mean-field type control problem which allows for random coefficients and may thus be non-Markovian.…
Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
Characteristic curves of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. However this description is valid only for smooth solutions. For nonsmooth "viscosity" solutions, which give rise to…