Slepoy A, Peters M D, Thompson A P
Multiscale Dynamic Materials Modeling Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
J Comput Chem. 2007 Nov 30;28(15):2465-71. doi: 10.1002/jcc.20710.
Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process, relying on expert physical intuition. To address this problem, a functional programming methodology was developed that may enable automated discovery of entirely new force-field functional forms, while simultaneously fitting parameter values. The method uses a combination of genetic programming, Metropolis Monte Carlo importance sampling and parallel tempering, to efficiently search a large space of candidate functional forms and parameters. The methodology was tested using a nontrivial problem with a well-defined globally optimal solution: a small set of atomic configurations was generated and the energy of each configuration was calculated using the Lennard-Jones pair potential. Starting with a population of random functions, our fully automated, massively parallel implementation of the method reproducibly discovered the original Lennard-Jones pair potential by searching for several hours on 100 processors, sampling only a minuscule portion of the total search space. This result indicates that, with further improvement, the method may be suitable for unsupervised development of more accurate force fields with completely new functional forms.
分子动力学和其他分子模拟方法依赖于仅基于原子核相对坐标的势能函数。这样一种函数，称为力场，近似地表示凝聚态物质系统的电子结构相互作用。开发这种近似函数并拟合其参数仍然是一个艰巨、耗时的过程，依赖于专家的物理直觉。为了解决这个问题，开发了一种函数式编程方法，该方法可以实现全新力场函数形式的自动发现，同时拟合参数值。该方法结合了遗传编程、 metropolis 蒙特卡罗重要性采样和平行回火，以有效地搜索候选函数形式和参数的大空间。使用一个具有明确全局最优解的非平凡问题对该方法进行了测试：生成了一小组原子构型，并使用 Lennard-Jones 对势计算了每个构型的能量。从一组随机函数开始，我们对该方法进行了完全自动化、大规模并行的实现，通过在100个处理器上搜索几个小时，仅对总搜索空间的极小一部分进行采样，可重复地发现了原始的 Lennard-Jones 对势。这一结果表明，经过进一步改进，该方法可能适用于无监督开发具有全新函数形式的更精确力场。
