A SQUARE ROOT APPROXIMATION OF TRANSITION RATES FOR A MARKOV STATE MODEL
Please always quote using this URN:urn:nbn:de:0296-matheon-13046
- Trajectory- or mesh-based methods for analyzing the dynamical behavior of large molecules tend to be impractical due to the curse of dimensionality - their computational cost increases exponentially with the size of the molecule. We propose a method to break the curse by a novel square root approximation of transition rates, Monte Carlo quadrature and a discretization approach based on solving linear programs. With randomly sampled points on the molecular energy landscape and randomly generated discretizations of the molecular con� guration space as our initial data, we construct a matrix describing the transition rates between adjacent discretization regions. This transition rate matrix yields a Markov State Model of the molecular dynamics. We use Perron cluster analysis and coarse-graining techniques in order to identify metastable sets in con� guration space and approximate the transition rates between the metastable sets. Application of our method to a simple energy landscape on a two-dimensional con� guration space provides proof of concept and an example for which we compare the performance of di� erent discretizations. We show that the computational cost of our method grows only polynomially with the size of the molecule. However, � nding discretizations of higher-dimensional con� guration spaces in which metastable sets can be identi� ed remains a challenge.
Author: | Han Cheng Lie, Konstantin Fackeldey, Marcus Weber |
---|---|
URN: | urn:nbn:de:0296-matheon-13046 |
Referee: | Benjamin Kunz |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2016/01/21 |
Release Date: | 2016/01/21 |
Institute: | Zuse Institute Berlin (ZIB) |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C99 None of the above, but in this section |
Preprint Number: | 1097 |