论文标题
动力学方程和相关问题的不确定性量化简介
An introduction to uncertainty quantification for kinetic equations and related problems
论文作者
论文摘要
我们概述了动力学方程的不确定性定量领域以及随机输入的相关问题的最新结果。不确定性可能是由于各种原因，例如缺乏有关微观交互细节的知识或在边界或初始数据上的不完整信息。这些不确定性有助于维度的诅咒，而有效的数值方法的发展是一个挑战。在对部分微分方程中不确定性定量的主要数值技术进行了简要介绍之后，我们将调查重点放在动力学方程的多效率方法和随机盖尔金方法上。
We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction details or incomplete information at the boundaries or on the initial data. These uncertainties contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. After a brief introduction on the main numerical techniques for uncertainty quantification in partial differential equations, we focus our survey on some of the recent progress on multi-fidelity methods and stochastic Galerkin methods for kinetic equations.
