论文标题
使用控制变体对Langevin动力学的移动性估计
Mobility estimation for Langevin dynamics using control variates
论文作者
论文摘要
由于摩擦的潜力消失，二维Langevin动力学在周期性潜力中的迁移率的缩放尚未得到很好的理解。缺乏理论上的结果，并且在阻尼不足的政权中的迁移率的数值计算是具有挑战性的，因为标准蒙特卡洛方法的计算成本与摩擦系数成反比，而确定性方法则不明显。在这项工作中，我们提出了一种基于控制变体的新方差减少方法，以有效地估算Langevin型动力学的迁移率。我们为提出的估计量的偏差和方差提供界限，并通过数值实验说明其疗效，首先是在简单的一维设置中，然后在二维Langevin Dynamics中进行说明。我们的结果证实了先前的数值证据，证明了在低摩擦方案中的迁移率的缩放性，具有简单的不可分割的潜力。
The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for non-separable potentials. Theoretical results are lacking, and numerical calculation of the mobility in the underdamped regime is challenging because the computational cost of standard Monte Carlo methods is inversely proportional to the friction coefficient, while deterministic methods are ill-conditioned. In this work, we propose a new variance-reduction method based on control variates for efficiently estimating the mobility of Langevin-type dynamics. We provide bounds on the bias and variance of the proposed estimator, and illustrate its efficacy through numerical experiments, first in simple one-dimensional settings and then for two-dimensional Langevin dynamics. Our results corroborate previous numerical evidence on the scaling of the mobility in the low friction regime for a simple non-separable potential.
