Deep Spectral Coarse Graining: Learning Simple, Dynamically Consistent Protein Models*

Coarse grain models of proteins offer promising gains in both computational efficiency for molecular simulations and the development of simple physical interpretations. Recent efforts have focused on formulating the development of coarse grained force fields as a supervised learning problem, taking advantage of deep learning techniques for handling highly non-linear multibody effects produced by imposing coarse grained representations. In this work, we present a deep learning method that utilizes spectral information from simulation data to preserve essential dynamics of the original system. Following a Koopman-motivated approach, we optimize the dynamical consistency between fine grain and coarse grain systems by forming a cost from the dynamical generator eigenequation. Through this method, we can recover coarse grain empirical free energy landscapes that preserve essential dynamical information from the fine grain system.