Schütte, Ch. and Winkelmann, S. and Hartmann, C. (2012) Optimal control of molecular dynamics using Markov state models. Math. Program. (Series B), 134 (1). pp. 259282.
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Official URL: http://dx.doi.org/10.1007/s1010701205476
Abstract
A numerical scheme for solving highdimensional 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 HamiltonJacobiBellman 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 coarsegrained 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 $\alpha$helices in an ensemble of small biomolecules (Alanine dipeptide), and discuss the relation to the large deviation principle of Donsker and Varadhan.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Other Institutes > Matheon > A  Life Sciences Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  1107 
Deposited By:  Carsten Hartmann 
Deposited On:  26 Oct 2011 12:51 
Last Modified:  03 Mar 2017 14:41 
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