Systematic Identification of Atom-Centered Symmetry Functions for the Development of Neural Network Potentials

Neural network potentials are emerging as promising classical force fields that can enable long-time and large-length scale simulations at close to ab initio accuracies. They learn the underlying potential energy surface by mapping the Cartesian coordinates of atoms to system energies using elemental neural networks. To ensure invariance with respect to system translation, rotation, and atom index permutations, in the Behler-Parrinnello type of neural network potential (BP-NNP), the Cartesian coordinates of atoms are transformed into "structural fingerprints" using atom-centered symmetry functions (ACSFs). Development of an accurate BP-NNP for any chemical system critically relies on the choice of these ACSFs. In this work, we have proposed a systematic framework for the identification of an optimal set of ACSFs for any target system, which not only considers the diverse atomic environments present in the training dataset but also inter-ACSF correlations. Our method is applicable to different kinds of ACSFs and across diverse chemical systems. We demonstrate this by building accurate BP-NNPs for water and Cu₂S systems.