Coarse-graining errors and numerical optimization using a relative entropy framework
Coarse-graining errors and numerical optimization using a relative entropy framework
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DOI：
10.1063/1.3557038
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发表时间：
2011-03-07
影响因子：
4.4
通讯作者：
Shell, M. Scott
中科院分区：
文献类型：
--
作者：
Chaimovich, Aviel;Shell, M. Scott
从参考全原子（或其他“第一原理”）模型生成精确的粗粒度模型的能力已经成为对具有大长度和时间尺度的复杂分子系统的行为进行建模的重要组成部分。我们最近提出了一种新的粗粒化方法的基础上变分最小化的配置空间功能称为相对熵，S-rel，测量粗粒化时丢失的信息。在这里，我们开发了一个广泛的理论框架，这种方法和数值策略，其使用在实际的粗粒度设置。特别是，我们表明，相对熵提供了严格的控制，由于粗粒化在任意微观性质的错误，并提出了一个系统的方法来减少它们。我们还描述了这种优化方法和其他粗粒度的策略，如逆蒙特卡罗，力匹配，能量匹配和变分平均场理论之间的基本连接。我们提出了几个新的数值方法，其最小化，提供新的粗粒度的战略。最后，我们证明了这些理论的考虑和算法的应用程序，一个简单的，有指导意义的系统和相对熵框架内的收敛性和错误的特点。(C)2011年美国物理学会。[doi 10.1063/1.3557038]
The ability to generate accurate coarse-grained models from reference fully atomic (or otherwise "first-principles") ones has become an important component in modeling the behavior of complex molecular systems with large length and time scales. We recently proposed a novel coarse-graining approach based upon variational minimization of a configuration-space functional called the relative entropy, S-rel, that measures the information lost upon coarse-graining. Here, we develop a broad theoretical framework for this methodology and numerical strategies for its use in practical coarse-graining settings. In particular, we show that the relative entropy offers tight control over the errors due to coarse-graining in arbitrary microscopic properties, and suggests a systematic approach to reducing them. We also describe fundamental connections between this optimization methodology and other coarse-graining strategies like inverse Monte Carlo, force matching, energy matching, and variational mean-field theory. We suggest several new numerical approaches to its minimization that provide new coarse-graining strategies. Finally, we demonstrate the application of these theoretical considerations and algorithms to a simple, instructive system and characterize convergence and errors within the relative entropy framework. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3557038]