School of Chemical Engineering, State University of Campinas, Campinas, Sao Paulo 13083-970, Brazil.
J Chem Phys. 2009 Oct 21;131(15):154113. doi: 10.1063/1.3245304.
Non-Boltzmann sampling (NBS) methods are usually able to overcome ergodicity issues which conventional Monte Carlo methods often undergo. In short, NBS methods are meant to broaden the sampling range of some suitable order parameter (e.g., energy). For many years, a standard for their development has been the choice of sampling weights that yield uniform sampling of a predefined parameter range. However, Trebst et al. [Phys. Rev. E 70, 046701 (2004)] demonstrated that better results are obtained by choosing weights that reduce as much as possible the average number of steps needed to complete a roundtrip in that range. In the present work, we prove that the method they developed to minimize roundtrip times also equalizes downtrip and uptrip times. Then, we propose a discrete-parameter extension using such isochronal character as our main goal. To assess the features of the new method, we carry out simulations of a spin system and of lattice chains designed to exhibit folding transition, thus being suitable models for proteins. Our results show that the new method performs on a par with the original method when the latter is applicable. However, there are cases in which the method of Trebst et al. becomes inapplicable, depending on the chosen order parameter and on the employed Monte Carlo moves. With a practical example, we demonstrate that our method can naturally handle these cases, thus being more robust than the original one. Finally, we find an interesting correspondence between the kind of approach dealt with here and the committor analysis of reaction coordinates, which is another topic of rising interest in the field of molecular simulation.
非玻尔兹曼抽样（NBS）方法通常能够克服传统蒙特卡罗方法经常遇到的遍历性问题。简而言之，NBS 方法旨在拓宽某些合适的序参量（例如能量）的采样范围。多年来，它们的发展标准一直是选择采样权重，以在预定义的参数范围内实现均匀采样。然而，Trebst 等人[Phys. Rev. E 70, 046701 (2004)]表明，通过选择权重来尽可能减少完成该范围内往返所需的平均步数，可以获得更好的结果。在本工作中，我们证明了他们开发的最小化往返时间的方法也可以使下行程和上行程时间相等。然后，我们提出了一种使用这种等时特征的离散参数扩展，作为我们的主要目标。为了评估新方法的特点，我们对自旋系统和晶格链进行了模拟，这些系统和晶格链旨在表现出折叠转变，因此是蛋白质的合适模型。我们的结果表明，在原始方法适用的情况下，新方法的性能与原始方法相当。然而，在某些情况下，取决于所选择的序参量和所采用的蒙特卡罗移动，Trebst 等人的方法变得不适用。通过一个实际例子，我们证明了我们的方法可以自然地处理这些情况，因此比原始方法更健壮。最后，我们发现这里处理的方法与反应坐标的占据分析之间存在有趣的对应关系，这是分子模拟领域另一个日益受到关注的话题。
