  We introduce a general framework for constructing coarse-grained potential
models without ad hoc approximations such as limiting the potential to two-
and/or three-body contributions. The scheme, called Deep Coarse-Grained
Potential (abbreviated DeePCG), exploits a carefully crafted neural network to
construct a many-body coarse-grained potential. The network is trained with
full atomistic data in a way that preserves the natural symmetries of the
system. The resulting model is very accurate and can be used to sample the
configurations of the coarse-grained variables in a much faster way than with
the original atomistic model. As an application we consider liquid water and
use the oxygen coordinates as the coarse-grained variables, starting from a
full atomistic simulation of this system at the ab-initio molecular dynamics
level. We found that the two-body, three-body and higher order oxygen
correlation functions produced by the coarse-grained and full atomistic models
agree very well with each other, illustrating the effectiveness of the DeePCG
model on a rather challenging task.
