  We present a scalable machine learning (ML) model to predict local electronic
properties such as on-site electron number and double occupation for disordered
correlated electron systems. Our approach is based on the locality principle,
or the nearsightedness nature, of many-electron systems, which means local
electronic properties depend mainly on the immediate environment. A ML model is
developed to encode this complex dependence of local quantities on the
neighborhood. We demonstrate our approach using the square-lattice
Anderson-Hubbard model, which is a paradigmatic system for studying the
interplay between Mott transition and Anderson localization. We develop a
lattice descriptor based on group-theoretical method to represent the on-site
random potentials within a finite region. The resultant feature variables are
used as input to a multi-layer fully connected neural network, which is trained
from datasets of variational Monte Carlo (VMC) simulations on small systems. We
show that the ML predictions agree reasonably well with the VMC data. Our work
underscores the promising potential of ML methods for multi-scale modeling of
correlated electron systems.
