The objective of molecular dynamics computations is to infer macroscopic properties of matter from atomistic models via averages with respect to probability measures dictated by the principles of statistical physics. Obtaining accurate results requires efficient sampling of atomistic configurations, which are typically generated using very long trajectories of stochastic differential equations in high dimensions, such as Langevin dynamics and its overdamped limit. Depending on the quantities of interest at the macroscopic level, one may also be interested in dynamical properties computed from averages over paths of these dynamics.This review describes how techniques from the analysis of partial differential equations can be used to devise good algorithms and to quantify their efficiency and accuracy. In particular, a crucial role is played by the study of the long-time behaviour of the solution to the Fokker–Planck equation associated with the stochastic dynamics.

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分子动力学中的偏微分方程和随机方法

分子动力学计算的目标是通过关于统计物理学原理所规定的概率测量的平均值从原子模型中推断出物质的宏观性质。获得准确的结果需要对原子配置进行有效采样，这些配置通常使用非常长的高维随机微分方程轨迹生成，例如朗之万动力学及其过阻尼极限。根据宏观水平上感兴趣的数量，人们也可能对从这些动力学路径上的平均值计算出的动力学特性感兴趣。这篇综述描述了如何使用偏微分方程分析中的技术来设计好的算法和量化他们的效率和准确性。特别是，