Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders

Molecular dynamics (MD) simulations have long been an important tool for studying molecular systems by providing atomistic insight into physicochemical processes that cannot be easily obtained through experimentation. A key step in extracting kinetic information from molecular simulation is the recovery of the slow dynamical modes that govern the longtime evolution of system coordinates within a low-dimensional latent space. The variational approach to conformational dynamics (V AC) [1, 2] has been successful in providing a mathematical framework through which the eigenfunctions of the underlying transfer operator can be estimated [3, 4]. A special case of V AC which estimates linearly optimal slow modes from mean-free input coordinates is known as time-lagged independent component analysis (TICA) [1, 2, 4-9]. TICA is a widely used approach that has become a standard step in the Markov state modeling pipeline [10]. However, it is restricted to form linear combinations of the input coordinates and is unable to learn nonlinear transformations that are typically required to recover high resolution kinetic models of all but the simplest molecular systems. Schwantes et al. address this limitation by applying the kernel trick with TICA to learn nonlinear functions of the input coordinates [11]. A special case of a radial basis function kernels was realized by No e and Nuske in the direct application of V AC using Gaussian functions [1]. Kernel TICA (kTICA), however, suffers from a number of drawbacks that have precluded its broad adoption.