Accurate and Data-Efficient Machine Learning Force Fields for Periodic Systems

It remains a substantial challenge to develop machine learning force fields that combine accuracy, efficiency, and physical interpretability, especially for complex periodic systems. In this work, we present an extension of the symmetrized gradient-domain machine learning (sGDML) framework [1][2] for periodic systems, which allows the construction of accurate molecular force fields with high data efficiency. We test this implementation in a variety of systems, including 2D materials, bulk materials and surfaces, for which we achieved errors of less than 1 kcal/mol/Å for atomic forces using less than 100 training points. Furthermore, in the particular case of graphene this error was achieved training on 20 samples. The low errors from sGDML calculations on phonon dispersion relations and thermodynamic properties compared to those obtained directly from DFT further confirm the predictive power of the model. These results extend the applicability of machine learning to increasingly complex periodic materials.

[1] Chmiela et al. Sci. Adv. 3 (5), e1603015 (2017); Nat. Commun. 9 (1), 3887 (2108); Comput. Phys. Commun. 240, 38 (2019).
[2] Sauceda et al. J. Chem. Phys. 150 (11), 114102 (2019); arXiv:1909.08565 (2019).