Impact of Derivative Observations on Gaussian Process Machine Learning Potentials: A Direct Comparison of Three Modeling Approaches

Machine learning (ML) potentials have become a well-established tool for providing inexpensive, yet quantum-mechanically accurate, atomistic simulations. Here, we extend our current modeling procedure, based on Gaussian process regression, to include derivative observations into the ML models. We directly compare three system-energy modeling approaches based on quantum mechanically derived quantities: (i) atomic energies, (ii) total system energy, and (iii) total system energy with derivative observations. We find that modeling the total energy with derivative observations has the best performance across the board, achieving chemical accuracy with fewer training data. In addition, both energy and force errors are around an order of magnitude lower when derivative observations are added to the models in some cases. We follow up with a discussion on the multiple advantages the proposed method of modeling brings, such as improved data set availability and the ability to easily include dispersion interactions. Additionally, we discuss the use cases of the new modeling approach in the ML force field FFLUX.