Nonlocal neural-network distillation of many-electron density functional theory*

Density functional theory (DFT) has offered a desirable balance of computational efficiency and quantitative accuracy in practical many-electron calculations for decades. Its central component, the exchange-correlation energy functional, has been approximated with increasing levels of complexity ranging from strictly local density approximations to nonlocal and orbital-dependent expressions with many empirically tuned parameters. In this work, we formulate a general way of rewriting complex density functionals using deep neural networks in a way that allows efficient computation of forces and Kohn-Sham potentials through automatic differentiation. These goals are achieved by introducing a novel class of convolutional neural network models capable of explicitly modeling functionals, as opposed to functions, while explicitly enforcing spatial symmetries. Functionals treated in this way are then called global density approximations and can be seamlessly integrated with existing DFT workflows. Tests are performed for a series of molecules and popular density functionals.