(330h) Variational Autoencoders As a Unifying Framework for Molecular Coarse Graining, Back-Mapping, and on-the-Fly Learning of Efficient Monte Carlo Moves

Bottom-up coarse graining enables simulations of nanoscale processes, such as self-assembly, that occur on long time and length scales relative to intramolecular vibrations and reconfigurations. Typically, degrees of freedom are grouped together (e.g., the atoms of an amino acid side chain) or simply removed, leaving behind only effective interactions between remaining groups (e.g., implicit solvent). It is difficult, however, to implicitly model solvent-mediated interactions, such as hydrophobic attractions, that involve a complex, many-body response of solvent molecules to solutes. As a result, information loss is inevitable during the coarse graining process, with resulting structural and thermodynamic differences from the fine-grained model difficult to assess. We apply variational autoencoders (VAEs) to the problem of coarse graining and back-mapping, demonstrating that this framework enables Monte Carlo moves that pass through and sample within a learned coarse-grained space while exactly preserving the original fine-grained ensemble of interest. In fact, we show that the acceptance rates of these moves approach unity for a perfect VAE model. While this is never observed in practice, VAE-based Monte Carlo moves still enhance sampling of new configurations. However, assumptions concerning the form of the encoding and decoding distributions, in particular the extent to which the decoder reflects the underlying physics, greatly impact the performance of the trained VAE. In conjunction, we also demonstrate that the learned coarse-grained model itself depends on the forms of both the encoder and decoder, with far-reaching implications for coarse graining as well as utilization of autoencoders within molecular simulation.