A coarse-grained deep neural network model for liquid water

We introduce a coarse-grained deep neural network (CG-DNN) model 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 the molecular forces of water, within 0.9 meV/molecule and 54 meV/Å 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 those 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 a fully flexible neural network framework that can subsequently be trained against sparse data from high-fidelity albeit expensive beyond-DFT calculations.