粗粒度动力学蒙特卡洛方法的误差分析
Error analysis of coarse-grained kinetic Monte Carlo method
AI总结：
本文研究粗粒度过程应用于晶格随机动力学动力学蒙特卡洛模拟的逼近性质，通过分析和数值证据表明粗模型层次结构允许在瞬态和长时间模拟中控制误差，并证明CGMC算法的数值精度在粗粒度比上为二阶，误差估计在弱收敛意义下成立，同时展示了在成核、相变和亚稳态等计算需求场景中的CPU加速。
摘要：
本文研究了应用于晶格随机动力学动力学蒙特卡洛模拟的粗粒度过程的逼近性质。我们提供了分析和数值证据，表明粗模型层次结构以系统的方式构建，允许在瞬态和长时间模拟中进行误差控制。我们证明了CGMC算法作为随机晶格自旋翻转动力学近似的数值精度在粗粒度比上为二阶，且自然小参数是粗粒度比与粒子/粒子相互作用范围的比值。误差估计在弱收敛意义下成立。我们利用推导的分析结果指导CGMC算法，并在涉及成核、相变和亚稳态的计算需求场景中展示了CPU加速。
英文摘要：
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for error control in both transient and long-time simulations. We demonstrate that the numerical accuracy of the CGMC algorithm as an approximation of stochastic lattice spin flip dynamics is of order two in terms of the coarse-graining ratio and that the natural small parameter is the coarse-graining ratio over the range of particle/particle interactions. The error estimate is shown to hold in the weak convergence sense. We employ the derived analytical results to guide CGMC algorithms and we demonstrate a CPU speed-up in demanding computational regimes that involve nucleation, phase transitions and metastability.
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