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

Nüske, Feliks; Schneider, Reinhold; Vitalini, Francesca; Noé, Frank

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.