Stochastic dynamical low-rank approximation method

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 eq...

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Bibliographic Details
Published inJournal of computational physics Vol. 372; pp. 564 - 586
Main Authors Cao, Yu, Lu, Jianfeng
Format Journal Article
LanguageEnglish
Published Cambridge Elsevier Inc 01.11.2018
Elsevier Science Ltd
Subjects
Approximation
Burgers equation
Computational physics
Differential equations
Dynamical low-rank approximation
Error analysis
Lindblad equation
Mathematical analysis
Model reduction
Stochastic differential equation
Stochastic models
Dynamical low-rank approximation
Lindblad equation
Model reduction
Stochastic differential equation
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Summary: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. •Propose stochastic dynamical low-rank approximation method to solve high-dimensional SDEs.•Provide a unified picture to discuss low-rank approximation for both Fokker–Planck equation and Lindblad equation.•Provide a commuting diagram connecting both low-rank approximation method and stochastic unraveling method for Lindblad equation.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.06.058