  The dynamics of physical systems that require high-dimensional representation
can often be captured in a few meaningful degrees of freedom called collective
variables (CVs). However, identifying CVs is challenging and constitutes a
fundamental problem in physical chemistry. This problem is even more pronounced
when CVs information about slow kinetics related to rare transitions between
long-lived metastable states. To address this issue, we propose an unsupervised
deep-learning method called spectral map. Our method constructs slow CVs by
maximizing the spectral gap between slow and fast eigenvalues of a transition
matrix estimated by an anisotropic diffusion kernel. We demonstrate our method
in several high-dimensional reversible folding processes.
