Accuracy evaluation of different machine learning force field features

Abstract Predicting energies and forces using machine learning force field (MLFF) depends on accurate descriptions (features) of chemical environment. Despite the numerous features proposed, there is a lack of controlled comparison among them for their universality and accuracy. In this work, we compared several commonly used feature types for their ability to describe physical systems. These different feature types include cosine feature, Gaussian feature, moment tensor potential (MTP) feature, spectral neighbor analysis potential feature, simplified smooth deep potential with Chebyshev polynomials feature and Gaussian polynomials feature, and atomic cluster expansion feature. We evaluated the training root mean square error (RMSE) for the atomic group energy, total energy, and force using linear regression model regarding to the density functional theory results. We applied these MLFF models to an amorphous sulfur system and carbon systems, and the fitting results show that MTP feature can yield the smallest RMSE results compared with other feature types for either sulfur system or carbon system in the disordered atomic configurations. Moreover, as an extending test of other systems, the MTP feature combined with linear regression model can also reproduce similar quantities along the ab initio molecular dynamics trajectory as represented by Cu systems. Our results are helpful in selecting the proper features for the MLFF development.