7065
2018
eng
425201
425201
42
30
article
0
--
--
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Estimation of the infinitesimal generator by square-root approximation
In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is—from a mathematical point of view—an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.
J. Phys.: Condens. Matter
10.1088/1361-648X/aadfc8
yes
2018-09-07
Luca Donati
Marcus Weber
Martin Heida
Bettina G. Keller
Marcus Weber
Numerical Mathematics
Weber, Marcus
SFB1114-A5
6595
2018
eng
A653
A670
18
2
40
article
0
2018-03-01
2018-02-01
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An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates
In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities.
SIAM Journal on Scientific Computing
yes
urn:nbn:de:0297-zib-62075
2017-11-17
Jannes Quer
Julia Boltze
Luca Donati
Bettina Keller
Marcus Weber
Numerical Mathematics
Computational Molecular Design
Weber, Marcus
SFB1114-A5
Quer, jannes