  In this work we propose an artificial neural network functional to the
ground-state energy of fermionic interacting particles in homogeneous chains
described by the Hubbard model. Our neural network functional was proven to has
an excellent performance: it deviates from numerically exact calculations by
less than $0.15\%$ for all the regimes of filling factors and magnetizations,
and for a vast regime of interactions. When compared to analytical functionals,
the neural functional was found to be more precise for all the regimes of
parameters, being particularly superior at the weakly interacting regime: where
the analytical parametrization fails the most, $\sim7\%$, against only
$\sim0.1\%$ for the neural functional. We have also applied our homogeneous
functional to finite, localized impurities and harmonically confined systems
within density-functional theory (DFT) methods. The results show that while our
artificial neural network approach is substantially more accurate than other
equivalently simple and fast DFT treatments, it has similar performance than
more costly DFT calculations and other independent many-body calculations, at a
fraction of the computational cost.
