A kernel-based method for coarse graining complex dynamical systems

Many of the dynamical processes investigated in the sciences today are characterized by the existence of phenomena on multiple, interconnected time scales that determine the longterm behavior of the process. Examples include the inherently multiscale dynamics of atmospheric vortex-and current formation which needs to be considered for effective weather prediction [24, 29], or the vast difference in time scales on which bounded atomic interactions, side-chain interactions, and the resulting formation of structural motifs occur in biomolecules [19, 12, 10]. An effective approach to analyzing these systems is often the identification of a low-dimensional observable of the system that captures the interesting behaviour on the longest time scale. However, the computerized identification of such observables from simulation data poses a significant computational challenge, especially for high-dimensional systems. Recently, the authors have developed a novel mathematical framework for identifying such essential observables for the slowest time scale of a system [6].