Pair-distribution-function guided optimization of fingerprints for atom-centered neural network potentials

Atom-centered neural network (ANN) potentials have shown promise in computational simulations and are recognized as both efficient and sufficiently accurate to describe systems involving bond formation and breaking. A key step in the development of ANN potentials is to represent atomic coordinates as suitable inputs for a neural network, commonly described as fingerprints. The accuracy and efficiency of the ANN potentials depend strongly on the selection of these fingerprints. Here, we propose an optimization strategy of atomic fingerprints to improve the performance of ANN potentials. Specifically, a set of fingerprints is optimized to fit a set of pre-selected template functions in the f^*g space, where f and g are the fingerprint and the pair distribution function for each type of interatomic interaction (e.g., a pair or 3-body). With such an optimization strategy, we have developed an ANN potential for the Pd₁₃H₂ nanoparticle system that exhibits a significant improvement to the one based upon standard template functions. We further demonstrate that the ANN potential can be used with the adaptive kinetic Monte Carlo method, which has strict requirements for the smoothness of the potential. The algorithm proposed here facilitates the development of better ANN potentials, which can broaden their application in computational simulations.