This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our goal is to provide an accessible and lively introduction to some core ideas, emphasizing that gradient flows uncover the conceptual unity behind many optimization and sampling algorithms, and that they give a rich mathematical framework for their rigorous analysis.

翻译：本文概述了梯度流动及其离散性如何有助于设计和分析优化和抽样算法。 优化、抽样和梯度流动之间的相互作用是一个积极的研究领域;我们的目标是为一些核心想法提供一个无障碍和生动的介绍,强调梯度流动揭示了许多优化和抽样算法背后的概念统一性,并为严格分析这些算法提供了丰富的数学框架。