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

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

Inst. Mathematik

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.