  We utilize connections between molecular coarse-graining approaches and
implicit generative models in machine learning to describe a new framework for
systematic molecular coarse-graining (CG). Focus is placed on the formalism
encompassing generative adversarial networks. The resulting method enables a
variety of model parameterization strategies, some of which show similarity to
previous CG methods. We demonstrate that the resulting framework can rigorously
parameterize CG models containing CG sites with no prescribed connection to the
reference atomistic system (termed virtual sites); however, this advantage is
offset by the lack of a closed-form expression for the CG Hamiltonian at the
resolution obtained after integration over the virtual CG sites. Computational
examples are provided for cases in which these methods ideally return identical
parameters as Relative Entropy Minimization (REM) CG but where traditional REM
CG optimization equations are not applicable.
