Stochastic dynamical low-rank approximation method

被引：5

作者：

Cao, Yu ^{[1
]}

Lu, Jianfeng ^{[1
,2
,3
]}

机构：

[1] Duke Univ, Dept Math, Box 90320, Durham, NC 27708 USA

[2] Duke Univ, Dept Phys, Box 90320, Durham, NC 27708 USA

[3] Duke Univ, Dept Chem, Box 90320, Durham, NC 27708 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2018年 / 372卷

基金：

美国国家科学基金会;

关键词：

Dynamical low-rank approximation; Stochastic differential equation; Lindblad equation; Model reduction; BIORTHOGONAL METHOD; SEMIGROUPS; SYSTEMS;

D O I：

10.1016/j.jcp.2018.06.058

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stochastic differential equations (SDEs) coming from classical stochastic dynamics or unraveling of Lindblad quantum master equations. We justify the proposed method by error analysis and also numerical examples for applications in solving high-dimensional SDE, stochastic Burgers' equation, and high-dimensional Lindblad equation. (C) 2018 Elsevier Inc. All rights reserved.

引用

收藏

页码：564 / 586

页数：23

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