Understanding Machine-learned Density Functionals
  Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densities} are found via a modified Euler-Lagrange constrained minimization of the total energy. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine-learned density functional approximations are discussed. 
Li Li, John C. Snyder, Isabelle M. Pelaschier, Jessica Huang,   Uma-Naresh Niranjan, Paul Duncan, Matthias Rupp, Klaus-Rober...
physics.chem-ph cs.LG physics.comp-ph stat.ML