Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation.

We propose a simple, but efficient and accurate, machine learning (ML) model for developing a high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in the condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level.