Finding Density Functionals with Machine Learning
  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. 
John C. Snyder, Matthias Rupp, Katja Hansen, Klaus-Robert M\"uller,   and Kieron Burke
physics.comp-ph cs.LG physics.chem-ph stat.ML