Stochastic dynamical low-rank approximation method
Provides a novel method for reducing computational cost in high-dimensional stochastic and quantum dynamics, but validation is limited to specific examples.
The authors extend dynamical low-rank approximation to signed measures, deriving stochastic low-rank dynamics for SDEs and Lindblad equations, with error bounds and numerical validation on high-dimensional problems.
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.