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Preprint 30-2015

Variational Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Feliks Nüske , Reinhold Schneider , Francesca Vitalini , Frank Noé

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 30-2015

MSC 2000

92-08 Computational methods

Abstract :
Essential information about the stationary and slow kinetic properties of macromolecules is contained in the eigenvalues and eigenfunctions of the dynamical operator of the molecular dynamics. A recent variational formulation allows to optimally approximate these eigenvalues and eigenfunctions when a basis set for the eigenfunctions is provided. In this study, we propose that a suitable choice of basis functions is given by products of one-coordinate basis functions, which describe changes along internal molecular coordinates, such as dihedral angles or distances. A sparse tensor product approach is employed in order to avoid a combinatorial explosion of products, i.e. of the basis-set size. Our results suggest that the high-dimensional eigenfunctions can be well approximated with relatively small basis set sizes.

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