Coulombic atomic descriptor for machine learning applications in condensed matter physics

A main class of machine learning approaches aims at predicting a label or value of some quantity from a set of input data (e.g., recognizing a face from the pixels of a digital image). As an example of the application of such techniques in computational condensed matter physics, we demonstrate here an accurate prediction of the atomic contributions into some physical quantity from the arrangement of neighboring atoms. We introduce a descriptor that quantifies the environment of each atom and is filled by the eigenvalues of an approximate Coulomb matrix. The descriptor is invariant under rotation or translation of the molecule and the permutation of the atomic indices. It captures fine structural deformations including the change of the four-body, dihedral angles. Employing this atomic descriptor, we exemplify a promising case where the charges on different atomic species in the molecule are predicted my machine learning to within one tenth of the elementary charge.