A neural network potential with self-trained atomic fingerprints: a test with the mW water potential

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. In addition to simplifying the selection of the atomic fingerprints, this strategy can also considerably improve the overall accuracy of the network representation. 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, largely 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.