  Orbital-free density functional theory (OF-DFT) holds the promise to compute
ground state molecular properties at minimal cost. However, it has been held
back by our inability to compute the kinetic energy as a functional of the
electron density only. We here set out to learn the kinetic energy functional
from ground truth provided by the more expensive Kohn-Sham density functional
theory. Such learning is confronted with two key challenges: Giving the model
sufficient expressivity and spatial context while limiting the memory footprint
to afford computations on a GPU; and creating a sufficiently broad distribution
of training data to enable iterative density optimization even when starting
from a poor initial guess. In response, we introduce KineticNet, an equivariant
deep neural network architecture based on point convolutions adapted to the
prediction of quantities on molecular quadrature grids. Important contributions
include convolution filters with sufficient spatial resolution in the vicinity
of the nuclear cusp, an atom-centric sparse but expressive architecture that
relays information across multiple bond lengths; and a new strategy to generate
varied training data by finding ground state densities in the face of
perturbations by a random external potential. KineticNet achieves, for the
first time, chemical accuracy of the learned functionals across input densities
and geometries of tiny molecules. For two electron systems, we additionally
demonstrate OF-DFT density optimization with chemical accuracy.
