Error and efficiency of simulated tempering simulations.
Error and efficiency of simulated tempering simulations.
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DOI：
10.1063/1.3290767
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发表时间：
2010-01
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影响因子：
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通讯作者：
E. Rosta;G. Hummer
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文献类型：
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作者：
E. Rosta;G. Hummer
我们推导出简单的解析表达式的误差和模拟回火（ST）模拟的计算效率。该理论适用于系统动态长期由两个亚稳态之间的缓慢相互转换主导的重要情况。描述了多状态情况的扩展。我们表明，ST模拟的效率相对于常规分子动力学（MD）或蒙特卡罗（MC）模拟的相对增益是由它们的反应通量之比给出的，即，在所有ST温度下两种状态之间的转换次数之和除以MD或MC模拟的单个温度下的转换次数。这种效率的关系是针对ST温度的变化与两态转换相比是快速的极限导出的。在这种情况下，ST是最有效的。我们对ST模拟的最大效率增益的表达式基本上与我们对副本交换MD和MC模拟导出的相应表达式相同[E.罗斯塔和G. Hummer，J.Chem.Phys.131，165102（2009）]。我们发现预测和观察到的效率增益之间的定量协议在测试中对ST和副本交换MC模拟的二维伊辛模型。基于效率公式，我们提供了ST模拟参数的最佳选择的建议，特别是温度的范围和数量，以及尝试温度变化的频率。
We derive simple analytical expressions for the error and computational efficiency of simulated tempering (ST) simulations. The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. An extension to the multistate case is described. We show that the relative gain in efficiency of ST simulations over regular molecular dynamics (MD) or Monte Carlo (MC) simulations is given by the ratio of their reactive fluxes, i.e., the number of transitions between the two states summed over all ST temperatures divided by the number of transitions at the single temperature of the MD or MC simulation. This relation for the efficiency is derived for the limit in which changes in the ST temperature are fast compared to the two-state transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived by us for replica exchange MD and MC simulations [E. Rosta and G. Hummer, J. Chem. Phys. 131, 165102 (2009)] on a different route. We find quantitative agreement between predicted and observed efficiency gains in a test against ST and replica exchange MC simulations of a two-dimensional Ising model. Based on the efficiency formula, we provide recommendations for the optimal choice of ST simulation parameters, in particular, the range and number of temperatures, and the frequency of attempted temperature changes.