John Strahan, Chatipat Lorpaiboon, Jonathan Weare, Aaron R Dinner
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引用次数: 0
摘要
分子动力学模拟的一个问题是,感兴趣的事件所涉及的时间尺度往往比模拟时间步长得多,而模拟时间步是由模型的最快时间尺度设定的。由于这种时标分离,直接模拟许多事件的计算成本过高。要解决这个问题,可以从许多相对较短的模拟中汇总信息,对涉及相关事件的轨迹片段进行采样。这是马尔可夫状态模型(MSM)和相关方法的策略,但由于定义状态的变量通常不能完全捕捉动态,因此这类方法存在近似误差。相比之下,加权集合(WE)方法一旦收敛,就会汇总来自轨迹片段的信息,从而对热力学和动力学统计进行无偏估计。遗憾的是,在最初制定和普遍采用的加权集合法中,误差衰减的速度并不比无偏模拟快。在这里,我们介绍了一种描述 WE 的理论框架,它表明在分层之上引入近似静态分布(如非平衡伞状采样(NEUS))可加速收敛。基于 MSMs 和相关方法的思想,我们对 NEUS 方法进行了概括,从而系统地减少了近似误差。我们的研究表明,改进后的算法可以将达到理想精度所需的模拟时间减少几个数量级。
An issue for molecular dynamics simulations is that events of interest often involve timescales that are much longer than the simulation time step, which is set by the fastest timescales of the model. Because of this timescale separation, direct simulation of many events is prohibitively computationally costly. This issue can be overcome by aggregating information from many relatively short simulations that sample segments of trajectories involving events of interest. This is the strategy of Markov state models (MSMs) and related approaches, but such methods suffer from approximation error because the variables defining the states generally do not capture the dynamics fully. By contrast, once converged, the weighted ensemble (WE) method aggregates information from trajectory segments so as to yield unbiased estimates of both thermodynamic and kinetic statistics. Unfortunately, errors decay no faster than unbiased simulation in WE as originally formulated and commonly deployed. Here, we introduce a theoretical framework for describing WE that shows that the introduction of an approximate stationary distribution on top of the stratification, as in nonequilibrium umbrella sampling (NEUS), accelerates convergence. Building on ideas from MSMs and related methods, we generalize the NEUS approach in such a way that the approximation error can be reduced systematically. We show that the improved algorithm can decrease the simulation time required to achieve the desired precision by orders of magnitude.
期刊介绍:
The Journal of Chemical Physics publishes quantitative and rigorous science of long-lasting value in methods and applications of chemical physics. The Journal also publishes brief Communications of significant new findings, Perspectives on the latest advances in the field, and Special Topic issues. The Journal focuses on innovative research in experimental and theoretical areas of chemical physics, including spectroscopy, dynamics, kinetics, statistical mechanics, and quantum mechanics. In addition, topical areas such as polymers, soft matter, materials, surfaces/interfaces, and systems of biological relevance are of increasing importance.
Topical coverage includes:
Theoretical Methods and Algorithms
Advanced Experimental Techniques
Atoms, Molecules, and Clusters
Liquids, Glasses, and Crystals
Surfaces, Interfaces, and Materials
Polymers and Soft Matter
Biological Molecules and Networks.