相关论文: Primal dual methods for Wasserstein gradient flows

A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…

We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…

We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem…

We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…

In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener…

Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…

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…

As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic particle methods are incompatible with diffusive partial…

Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…

This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…

In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…

This paper presents a Crank-Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization…

We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…

In this paper, based a novel primal-dual dynamical model with adaptive scaling parameters and Bregman divergences, we propose new accelerated primal-dual proximal gradient splitting methods for solving bilinear saddle-point problems with…

This paper presents a novel algorithmic study with extensive numerical experiments of distributionally robust multistage convex optimization (DR-MCO). Following the previous work on dual dynamic programming (DDP) algorithmic framework for…

The paper studies a time-nonlocal multiphysics finite element method with Crank-Nicolson scheme for poroelasticity model with secondary consolidation. For the case where the physical parameters $\lambda,\lambda^*$ and $c_0$ are all finite…

In this work, we present an efficient approach for the spatial and temporal discretization of the nonlocal Allen-Cahn equation, which incorporates various double-well potentials and an integrable kernel, with a particular focus on a…

Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

In this paper, we study the stability and convergence of a fully discrete finite difference scheme for the initial value problem associated with the Korteweg-De Vries (KdV) equation. We employ the Crank-Nicolson method for temporal…