Stochastic dynamical low-rank approximation method
arXiv:1803.00499 · doi:10.1016/j.jcp.2018.06.058
Abstract
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.
arXiv comment27 pages, 8 figures
References in corpus (4)
- Continuous measurements, quantum trajectories, and decoherent histories
- Low rank approximation for the numerical simulation of high dimensional Lindblad and Riccati equations
- Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations
- Quantum Damped Harmonic Oscillator
Cited by in corpus (5)
- Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases
- Structure-preserving numerical schemes for Lindblad equations
- Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory
- Dynamical Low-Rank Approximation for Stochastic Differential Equations
- Dynamically Optimal Unraveling Schemes for Simulating Lindblad Equations