Department of Chemistry and Applied Biosciences, ETH Zurich and Facoltà di Informatica, Instituto di Scienze Computationali, Università della Svizzera italiana, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland.
Phys Rev Lett. 2014 Aug 29;113(9):090601. doi: 10.1103/PhysRevLett.113.090601. Epub 2014 Aug 27.
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.
广泛使用的采样方法，如分子动力学或蒙特卡罗模拟，在探索复杂的自由能景观时，受到动力学瓶颈的严重阻碍。已经提出了大量的解决方案来缓解这个问题。许多方法都是基于引入一个偏压势，该势是少数几个集体变量的函数。然而，构建这样的偏压并不简单。在这里，我们引入了一个偏压势的泛函和一个相关的变分原理。最小化泛函的偏压势与自由能面有简单的关系。这个变分原理可以转化为一种实用、高效和灵活的采样方法。我们提出了一些数值例子，包括确定一个三维自由能面。我们认为，除了在数值上有优势之外，我们的变分方法还为采样问题提供了一个方便和新颖的观点。
