Symmetry Matters: Machine-learning of Scalar and Tensorial Atomic-Scale Properties

Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Bayesian statistical learning, combined with local descriptors of chemical environments, provides a unified framework to predict atomic-scale properties [1]. The framework is very general, and can be applied equally well to solids, surfaces, molecules and biological systems. It can predict molecular energetics with chemical accuracy and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of this framework provides new insight into the potential energy surface of materials and molecules. The method can also be extended to yield a "symmetry-adapted" Gaussian process regression [2] approach that is capable of learning efficiently tensorial properties by enforcing automatically the appropriate transformation rules. [1] A. P. Bartok, S. De, C. Poelking, N. Bernstein, J. Kermode, G. Csanyi, and M. Ceriotti, Sci. Adv. 3, e1701816 (2017). [2] A. Grisafi, D. M. Wilkins, G. Csányi, and M. Ceriotti, arXiv:1709.06757 (2018).