Spectral neural network potentials for binary alloys

In this work, we present a numerical implementation to compute the atom centered descriptors introduced by Bartok et al (Phys. Rev. B, 87, 184115, 2013) based on the harmonic analysis of the atomic neighbor density function. Specifically, we focus on two types of descriptors, the smooth SO(3) power spectrum with the explicit inclusion of a radial basis and the SO(4) bispectrum obtained through mapping the radial component onto a polar angle of a four dimensional hypersphere. With these descriptors, various interatomic potentials for binary Ni-Mo alloys are obtained based on linear and neural network regression models. Numerical experiments suggest that both descriptors produce similar results in terms of accuracy. For linear regression, the smooth SO(3) power spectrum is superior to the SO(4) bispectrum when a large band limit is used. In neural network regression, a better accuracy can be achieved with even less number of expansion components for both descriptors. As such, we demonstrate that spectral neural network potentials are feasible choices for large scale atomistic simulation.