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The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the atoms. In particular, atomic species, magnetic moments and charges are attached to the atomic positions and an atomic cluster expansion that includes the different degrees of freedom on equal footing is derived. Expressions for the efficient evaluation of forces and torques are given. Relations to other methods are discussed.
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process re
Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-lea
The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling properties of
Machine learning of atomic-scale properties is revolutionizing molecular modelling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed and reliability of machine-lear
Two-dimensional CrI3 has attracted much attention as it is reported to be a ferromagnetic semiconductor with the Curie temperature around 45K. By performing first-principles calculations, we find that the magnetic ground state of CrI3 is variable und