相关论文: Variational Wasserstein gradient flow

Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we adopt a probabilistic and variational point of view by considering a minimization problem in the space of probability measures…

Wasserstein gradient flow provides a general framework for minimizing an energy functional $J$ over the space of probability measures on a Riemannian manifold $(M,g)$. Its canonical time-discretization, the Jordan-Kinderlehrer-Otto (JKO)…

We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…

In order to sample from an unnormalized probability density function, we propose to combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. We relate the iterative training of CNFs with…

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…

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…

Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

Inspired by the gradient flow viewpoint of the Landau equation and the corresponding dynamic formulation of the Landau metric in [arXiv:2007.08591], we develop a novel implicit particle method for the Landau equation in the framework of the…

We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step $h>0$, a large-deviations rate functional $J_h$ characterizes the…

Wasserstein Policy Optimization (WPO) is a recently proposed reinforcement learning algorithm that leverages Wasserstein gradient flows to optimize stochastic policies in continuous action spaces. Despite its empirical success, the…

As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…

Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving…

Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does…

In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of $q$-Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically…

Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. However, the design of…

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapping functions of gradient flows by the class of two-layer…