马尔可夫状态模型再探讨：无偏可观测量的原理与算法
Markov state models revisited: Principles and algorithms for unbiased observables
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中文总结 AI 辅助
本文针对马尔可夫状态模型，指出标准框架存在可避免的模型偏差。提出用两个转移矩阵取代单矩阵框架的方法，能在无限且加权适当的数据极限下，于任何固定滞后时间和粗粒度下获得无偏的粗粒度可观测量。
中文摘要 AI 辅助
马尔可夫状态模型（MSMs）因其简单而强大的前提，成为分析分子动力学（MD）模拟的常用工具：尽管完整的MD采样可能无法实现，但MSM可以“拼接”从局部采样得出的转移概率，以提供动力学和机制的全局图景。在标准MSM框架中，可用的MD数据被组织成单个转移矩阵，然后用于估计在选定滞后时间的所有可观测量，以使粗粒度动力学近似为马尔可夫过程。这种方法会导致可避免的模型偏差，并促使使用长滞后时间，从而掩盖了感兴趣的短时间尺度过程。相比之下，本文展示了在无限且加权适当的数据极限下，如何在任何固定滞后时间和任何固定粗粒度下获得无偏的粗粒度可观测量。核心思想是用两个转移矩阵取代单矩阵框架——一个代表平衡动力学，另一个代表源汇循环动力学——并使用正确的一个或多个矩阵来估计匹配的动力学可观测量。
英文摘要
Markov state models (MSMs) have become ubiquitous tools for analyzing molecular dynamics (MD) simulations because of their simple, powerful premise: although complete MD sampling may be impossible, the MSM can "stitch together" transition probabilities derived from local sampling to provide a global picture of kinetics and mechanisms. In the standard MSM framework, the available MD data is organized into a single transition matrix, which is then used to estimate all observables at a lag time chosen so the coarse-grained dynamics are approximately Markovian. This approach leads to avoidable model bias and motivates long lag times that obscure short-timescale processes of interest. In contrast, this paper shows how to obtain unbiased coarse-grained observables at any fixed lag time and for any fixed coarse-graining in the limit of infinite, properly weighted data. The central idea is to replace the single-matrix framework with two transition matrices -- one representing equilibrium dynamics and another representing source-sink recycling dynamics -- and use the correct matrix or matrices to estimate the matched dynamical observables.
