  We present a neural network (NN) potential based on a new set of atomic
fingerprints built upon two- and three-body contributions that probe distances
and local orientational order respectively. Compared to existing NN potentials,
the atomic fingerprints depend on a small set of tuneable parameters which are
trained together with the neural network weights. To tackle the simultaneous
training of the atomic fingerprint parameters and neural network weights we
adopt an annealing protocol that progressively cycles the learning rate,
significantly improving the accuracy of the NN potential. We test the
performance of the network potential against the mW model of water, which is a
classical three-body potential that well captures the anomalies of the liquid
phase. Trained on just three state points, the NN potential is able to
reproduce the mW model in a very wide range of densities and temperatures, from
negative pressures to several GPa, capturing the transition from an open random
tetrahedral network to a dense interpenetrated network. The NN potential also
reproduces very well properties for which it was not explicitly trained, such
as dynamical properties and the structure of the stable crystalline phases of
mW.
