WIAS Preprint No. 2416, (2017)

Estimation of the infinitesimal generator by square-root approximation


  • Donati, Luca
  • Heida, Martin
    ORCID: 0000-0002-7242-8175
  • Weber, Marcus
  • Keller, Bettina

2008 Physics and Astronomy Classification Scheme

  • 02.50.Ga 05.10Gg


  • molecular simulation, Markov state models, transfer operator, molecular kinetics




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 approximated 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 correlation 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.

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