Repository: Freie Universit├Ąt Berlin, Math Department

Estimation of the infinitesimal generator by square-root approximation

Donati, L. and Heida, M. and Weber, M. and Keller, B. (2018) Estimation of the infinitesimal generator by square-root approximation. Journal of Physics: Condensed Matter, 30 (42). p. 425201. ISSN 0953-8984, ESSN: 1361-648X


Official URL: https://doi:10.1088/1361-648X/aadfc8


For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.

Item Type:Article
Additional Information:SFB 1114 Preprint 08/2017 im WIAS (2416)
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2167
Deposited By: Silvia Hoemke
Deposited On:19 Dec 2017 13:30
Last Modified:22 Feb 2022 17:29

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