Kohn-Sham regularizer for spin density functional theory and weakly correlated systems

Kohn-Sham regularizer (KSR) is a machine learning approach that optimizes a physics-informed exchange-correlation functional within a differentiable Kohn-Sham density functional theory (DFT) framework. We generalize KSR to spin DFT and create local, semilocal, and nonlocal approximations for the exchange-correlation functional. We explore KSR for weakly correlated systems, by training on atoms and testing on molecules at equilibrium. The generalization error from our semilocal approximation is comparable to other differentiable approaches. Our nonlocal functional outperforms any existing machine learning functionals by predicting the ground-state energies of the test systems with a mean absolute error of 2.7 milli-Hartrees.