Convolutional learning of electronic properties in disordered correlated materials

In recent years, deep learning (DL) has served as a powerful tool in the calculation of complex interatomic forces and potential energy surfaces within correlated materials. These methods forgo the nonlinear computational expenses required by popular techniques such as density functional theory and Hartree Fock. One approach involves the assumption that local electronic properties of a site depend almost entirely on an immediate, local neighborhood. Herein, we build on methods utilizing neural networks to learn the Gutzwiller (GW) solutions of Anderson-Hubbard square lattice models. Previous work focused on the use of a symmetry-invariant lattice descriptor to represent the on-site potentials of the lattice sites, which is taken as input to a fully connected network. We design a Convolutional Neural Network (CNN) that directly uses on-site potentials to predict electronic properties without symmetry-invariant inputs. We demonstrate that our CNN predictions agree reasonably with the GW approximation data, with inherently linear computational scaling. However, bypassing feature engineering significantly increases the amount of training data required to achieve competitive accuracy with previous methods. Here, we present a study of the tradeoff between DL approaches, with and without symmetry invariance, in efficiently learning the local electronic properties of correlated materials.