  Machine learning is used to approximate density functionals. For the model
problem of the kinetic energy of non-interacting fermions in 1d, mean absolute
errors below 1 kcal/mol on test densities similar to the training set are
reached with fewer than 100 training densities. A predictor identifies if a
test density is within the interpolation region. Via principal component
analysis, a projected functional derivative finds highly accurate
self-consistent densities. Challenges for application of our method to real
electronic structure problems are discussed.
