  We propose a systematic procedure for the approximation of density
functionals in density functional theory that consists of two parts. First, for
the efficient approximation of a general density functional, we introduce an
efficient ansatz whose non-locality can be increased systematically. Second, we
present a fitting strategy that is based on systematically increasing a
reasonably chosen set of training densities. We investigate our procedure in
the context of strongly correlated fermions on a one-dimensional lattice in
which we compute accurate training densities with the help of matrix product
states. Focusing on the exchange-correlation energy, we demonstrate how an
efficient approximation can be found that includes and systematically improves
beyond the local density approximation. Importantly, this systematic
improvement is shown for target densities that are quite different from the
training densities.
