Computation of Essential Molecular

The paper presents basic concepts of a new type of algorithm for the numerical computation of what the authors call the essential dynamics of molecular systems. Mathematically speaking, such systems are described by Hamiltonian diierential equations. In the bulk of applications, individual trajectories are of no speciic interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynami-cal systems, such information is contained in the natural invariant measure (innnite relaxation time) or in almost invariant sets ("large" nite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is diierent from both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by short term sub-trajectories, Monte-Carlo techniques are connected via the underlying Frobenius-Perron structure. Numerical experiments with the suggested algorithm are included to illustrate certain distinguishing properties .