Understanding Machine-learned Density Functionals

Understand

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.