Deringer, Volker L.Bartok, Albert P.Bernstein, NoamWilkins, David M.Ceriotti, MicheleCsanyi, Gabor2021-09-112021-09-112021-09-112021-08-2510.1021/acs.chemrev.1c00022https://infoscience.epfl.ch/handle/20.500.14299/181363WOS:000691784200009We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.Chemistry, MultidisciplinaryChemistrydensity-functional theoryphase-change materialspotential-energy surfacesmachine learning-modelsx-ray spectroscopyab-initioamorphous-carboninteratomic potentialselectron-densitycombining experimentstext::journal::journal article::review article