Beyond potentials: Integrated machine learning models for materials

Abstract Over the past decade, interatomic potentials based on machine learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure calculations, they inherit their predictive accuracy, and extend greatly the length and time scales that are accessible to explicit atomistic simulations. Inexpensive predictions of the energetics of individual configurations have facilitated greatly the calculation of the thermodynamics of materials, including finite-temperature effects and disorder. More recently, ML models have been closing the gap with first-principles calculations in another area: the prediction of arbitrarily complicated functional properties, from vibrational and optical spectroscopies to electronic excitations. The implementation of integrated ML models that combine energetic and functional predictions with statistical and dynamical sampling of atomic-scale properties is bringing the promise of predictive, uncompromising simulations of existing and novel materials closer to its full realization. Graphical abstract