  We introduce a coarse-grained deep neural network model (CG-DNN) for liquid
water that utilizes 50 rotational and translational invariant coordinates, and
is trained exclusively against energies of ~30,000 bulk water configurations.
Our CG-DNN potential accurately predicts both the energies and molecular forces
of water; within 0.9 meV/molecule and 54 meV/angstrom of a reference
(coarse-grained bond-order potential) model. The CG-DNN water model also
provides good prediction of several structural, thermodynamic, and temperature
dependent properties of liquid water, with values close to that obtained from
the reference model. More importantly, CG-DNN captures the well-known density
anomaly of liquid water observed in experiments. Our work lays the groundwork
for a scheme where existing empirical water models can be utilized to develop
fully flexible neural network framework that can subsequently be trained
against sparse data from high-fidelity albeit expensive beyond-DFT
calculations.
