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Computation 2018, 6(1), 22; https://doi.org/10.3390/computation6010022

Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics

1
Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
2
Zuse Institute Berlin, 14195 Berlin, Germany
*
Author to whom correspondence should be addressed.
Received: 12 January 2018 / Revised: 15 February 2018 / Accepted: 23 February 2018 / Published: 26 February 2018
(This article belongs to the Special Issue Computation in Molecular Modeling)
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Abstract

There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us noticing it, due to insufficient observations; and it even might be a system failing to admit an equilibrium distribution at all. We review some of the approaches that model the effective statistical behavior of equilibrium and non-equilibrium dynamical systems, and show that both cases can be considered under the unified framework of optimal low-rank approximation of so-called transfer operators. Particular attention is given to the connection between these methods, Markov state models, and the concept of metastability, further to the estimation of such reduced order models from finite simulation data. All these topics bear an important role in, e.g., molecular dynamics, where Markov state models are often and successfully utilized, and which is the main motivating application in this paper. We illustrate our considerations by numerical examples. View Full-Text
Keywords: Markov state model; non-equilibrium; metastability; coherent set; molecular dynamics; transfer operator; Koopman operator; extended dynamic mode decomposition Markov state model; non-equilibrium; metastability; coherent set; molecular dynamics; transfer operator; Koopman operator; extended dynamic mode decomposition
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Koltai, P.; Wu, H.; Noé, F.; Schütte, C. Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics. Computation 2018, 6, 22.

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