Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach

Molecular simulation is an important and ubiquitous tool in the study of microscopic phenomena in fields as diverse as materials science, protein folding and drug design. While the atomic-level resolution provides unparalleled detail, it can be non-trivial to extract the important motions underlying simulations of complex systems containing many degrees of freedom. The diffusion map is a nonlinear dimensionality reduction technique with the capacity to systematically extract the essential dynamical modes of high-dimensional simulation trajectories, furnishing a kinetically meaningful low-dimensional framework with which to develop insight and understanding of the underlying dynamics and thermodynamics. We survey the potential of this approach in the field of molecular simulation, consider its challenges, and discuss its underlying concepts and means of application. We provide examples drawn from our own work on the hydrophobic collapse mechanism of n-alkane chains, folding pathways of an antimicrobial peptide, and the dynamics of a driven interface.