Katsoulakis Markos A, Majda Andrew J, Vlachos Dionisios G
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA.
Proc Natl Acad Sci U S A. 2003 Feb 4;100(3):782-7. doi: 10.1073/pnas.242741499. Epub 2003 Jan 27.
Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.
从材料科学到催化、生物分子动力学再到气候建模等不同的科学学科，都涉及到在大范围具有物理意义的长度尺度上的非线性相互作用。在此，一类描述计算上可行的介观长度尺度的粗粒化随机过程及相应的蒙特卡罗模拟方法，是直接从微观晶格系统推导出来的。如下所示，粗粒化随机模型能够捕捉大规模结构，同时保留重要的微观信息。细致平衡的要求被用作一种系统的设计原则，以确保粗粒化模型具有正确的噪声涨落。与微观蒙特卡罗模拟相比，粗粒化随机算法在不增加编程复杂性或每次执行事件的计算机时间的情况下，实现了大量的计算节省。
