Optimal control of molecular dynamics using Markov state models
Optimal control of molecular dynamics using Markov state models
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使用马尔可夫状态模型优化分子动力学控制
DOI：
10.1007/s10107-012-0547-6
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发表时间：
2012
影响因子：
2.7
通讯作者：
C. Hartmann
中科院分区：
文献类型：
--
作者：
C. Schütte;S. Winkelmann;C. Hartmann
概述了在分子动力学背景下求解无限时间范围内高维随机控制问题的数值格式。该方案依赖于将相应的Hamilton-Jacobi-Bellman方程解释为一个非线性特征值问题，使用对数变换，可以将其重新转换为一个线性特征值问题，并寻求主特征值及其特征函数。后者可以通过对显性亚稳集的粗粒度马尔可夫状态模型近似底层随机过程来有效地计算。我们用两个数值例子来说明我们的方法，其中一个涉及到在小生物分子（丙氨酸二肽）的集合中最大化α-螺旋种群的任务，并讨论了与Donsker和Varadhan的大偏差原理的关系。
A numerical scheme for solving high-dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined. The scheme rests on the interpretation of the corresponding Hamilton–Jacobi–Bellman equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem, for which the principal eigenvalue and its eigenfunction are sought. The latter can be computed efficiently by approximating the underlying stochastic process with a coarse-grained Markov state model for the dominant metastable sets. We illustrate our method with two numerical examples, one of which involves the task of maximizing the population of α-helices in an ensemble of small biomolecules (alanine dipeptide), and discuss the relation to the large deviation principle of Donsker and Varadhan.
DOI：
10.1073/pnas.0600511103
发表时间：
2006-07-11
影响因子：
11.1
作者：
Jaeger, Marcus;Zhang, Yan;Kelly, Jeffery W.
通讯作者：
Kelly, Jeffery W.
影响因子：
4.4
作者：
Chodera, John D.;Singhal, Nina;Swope, William C.
通讯作者：
Swope, William C.