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Understanding Machine-learned Density Functionals (1404.1333v2)
Published 4 Apr 2014 in physics.chem-ph, cs.LG, physics.comp-ph, and stat.ML
Abstract: 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.