Learning (from) the Electron Density: Transferability, Conformational and Chemical Diversity

Machine-learning in quantum chemistry is currently booming, with reported applications spanning all molecular properties from simple atomization energies to complex mathematical objects such as the many-body wavefunction. Due to its central role in density functional theory, the electron density is a particularly compelling target for non-linear regression. Nevertheless, the scalability and the transferability of the existing machine-learning models of ρ(r) are limited by its complex rotational symmetries. Recently, in collaboration with Ceriotti and coworkers, we combined an efficient electron density decomposition scheme with a local regression framework based on symmetry-adapted Gaussian process regression able to accurately describe the covariance of the electron density spherical tensor components. The learning exercise is performed on local environments, allowing high transferability and linear-scaling of the prediction with respect to the number of atoms. Here, we review the main characteristics of the model and show its predictive power in a series of applications. The scalability and transferability of the trained model are demonstrated through the prediction of the electron density of Ubiquitin.