ESTIMATING THE EIGENVALUE ERROR OF MARKOV STATE MODELS
ESTIMATING THE EIGENVALUE ERROR OF MARKOV STATE MODELS
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DOI：
10.1137/100798910
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发表时间：
2012-01-01
影响因子：
1.6
通讯作者：
Schuette, Christof
中科院分区：
文献类型：
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作者：
Djurdjevac, Natasa;Sarich, Marco;Schuette, Christof
我们考虑一个大的连续或离散状态空间上的连续时间，遍历马尔可夫过程。该过程被假定为表现出一些亚稳态集。马尔可夫状态模型（MSMs）被设计成通过马尔可夫链来表示这样的过程的有效动态，该马尔可夫链在具有原始过程的转移率的亚稳态集之间跳跃。MSM已被用于许多应用，包括分子动力学（cf. [F. Noe等人，Proc. Natl. Acad. Sci. USA，106（2009），pp. 19011-19016年），超过十年。然而，对它们的近似质量的严格和全面的（没有零温度限制或类似的限制）分析只是最近才开始的。关于这个主题的第一篇文章[M]。Sarich，F. No ' e和Ch. Sch' utte，多尺度模型。同时，8（2010），pp. 1154-1177]引入了MSM和原始过程在长时间尺度上的概率密度传播差异的误差界。在这里，我们提供的MSM和原始过程之间的特征值的误差的上限，这意味着我们分析如何以及最长的时间尺度在原始过程中近似的MSM。我们的研究结果说明了数值实验。
We consider a continuous-time, ergodic Markov process on a large continuous or discrete state space. The process is assumed to exhibit a number of metastable sets. Markov state models (MSMs) are designed to represent the effective dynamics of such a process by a Markov chain that jumps between the metastable sets with the transition rates of the original process. MSMs have been used for a number of applications, including molecular dynamics (cf. [F. Noe et al., Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 19011-19016]), for more than a decade. The rigorous and fully general (no zero temperature limit or comparable restrictions) analysis of their approximation quality, however, has only recently begun. Our first article on this topics [M. Sarich, F. No ' e, and Ch. Sch " utte, Multiscale Model. Simul., 8 (2010), pp. 1154-1177] introduces an error bound for the difference in propagation of probability densities between the MSM and the original process on long timescales. Herein we provide upper bounds for the error in the eigenvalues between the MSM and the original process, which means that we analyze how well the longest timescales in the original process are approximated by the MSM. Our findings are illustrated by numerical experiments.