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This chapter discusses the importance of incorporating three-dimensionalsymmetries in the context of statistical learning models geared towards theinterpolation of the tensorial properties of atomic-scale structures. We focuson Gaussian process regression, and in particular on the construction ofstructural representations, and the associated kernel functions, that areendowed with the geometric covariance properties compatible with those of thelearning targets. We summarize the general formulation of such asymmetry-adapted Gaussian process regression model, and how it can beimplemented based on a scheme that generalizes the popular smooth overlap ofatomic positions representation. We give examples of the performance of thisframework when learning the polarizability and the ground-state electrondensity of a molecule.

Atomic-scale representation and statistical learning of tensorial properties