Mobility Estimation for Langevin Dynamics Using Control Variates

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Grigorios A. Pavliotis, G. Stoltz, Urbain Vaes
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引用次数: 0

Abstract

The scaling of the mobility of two-dimensional Langevin dynamics in a periodic potential as the friction vanishes is not well understood for nonseparable 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 prior numerical evidence that the mobility scales as , with , in the low friction regime for a simple nonseparable potential.
基于控制变量的朗格万动力学迁移率估计
当摩擦消失时,二维朗之万动力学在周期势中的迁移率的标度对于不可分离势还没有很好地理解。由于标准蒙特卡罗方法的计算成本与摩擦系数成反比,而确定性方法是病态的,因此缺乏理论结果,欠阻尼状态下迁移率的数值计算具有挑战性。在这项工作中,我们提出了一种新的基于控制变量的方差缩减方法来有效地估计朗万型动力学的迁移率。我们提供了所提出的估计器的偏差和方差的界限,并通过数值实验说明了它的有效性,首先在简单的一维设置中,然后在二维朗格万动力学中。我们的结果证实了先前的数值证据,即在简单的不可分离电位的低摩擦状态下,迁移率尺度为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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