  The properties of electrons in matter are of fundamental importance. They
give rise to virtually all molecular and material properties and determine the
physics at play in objects ranging from semiconductor devices to the interior
of giant gas planets. Modeling and simulation of such diverse applications rely
primarily on density functional theory (DFT), which has become the principal
method for predicting the electronic structure of matter. While DFT
calculations have proven to be very useful to the point of being recognized
with a Nobel prize in 1998, their computational scaling limits them to small
systems. We have developed a machine learning framework for predicting the
electronic structure on any length scale. It shows up to three orders of
magnitude speedup on systems where DFT is tractable and, more importantly,
enables predictions on scales where DFT calculations are infeasible. Our work
demonstrates how machine learning circumvents a long-standing computational
bottleneck and advances science to frontiers intractable with any current
solutions. This unprecedented modeling capability opens up an inexhaustible
range of applications in astrophysics, novel materials discovery, and energy
solutions for a sustainable future.
