  Small integration time steps limit molecular dynamics (MD) simulations to
millisecond time scales. Markov state models (MSMs) and equation-free
approaches learn low-dimensional kinetic models from MD simulation data by
performing configurational or dynamical coarse-graining of the state space. The
learned kinetic models enable the efficient generation of dynamical
trajectories over vastly longer time scales than are accessible by MD, but the
discretization of configurational space and/or absence of a means to
reconstruct molecular configurations precludes the generation of continuous
all-atom molecular trajectories. We propose latent space simulators (LSS) to
learn kinetic models for continuous all-atom simulation trajectories by
training three deep learning networks to (i) learn the slow collective
variables of the molecular system, (ii) propagate the system dynamics within
this slow latent space, and (iii) generatively reconstruct molecular
configurations. We demonstrate the approach in an application to Trp-cage
miniprotein to produce novel ultra-long synthetic folding trajectories that
accurately reproduce all-atom molecular structure, thermodynamics, and kinetics
at six orders of magnitude lower cost than MD. The dramatically lower cost of
trajectory generation enables greatly improved sampling and greatly reduced
statistical uncertainties in estimated thermodynamic averages and kinetic
rates.
