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Kohn-Sham regularizer (KSR) is a differentiable machine learning approach tofinding the exchange-correlation functional in Kohn-Sham density functionaltheory (DFT) that works for strongly correlated systems. Here we test KSR forweak correlation. We propose spin-adapted KSR (sKSR) with trainable local,semilocal, and nonlocal approximations found by minimizing density and totalenergy loss. We assess the atoms-to-molecules generalizability by training onone-dimensional (1D) H, He, Li, Be, Be$^{++}$ and testing on 1D hydrogenchains, LiH, BeH$_2$, and helium hydride complexes. The generalization errorfrom our semilocal approximation is comparable to other differentiableapproaches, but our nonlocal functional outperforms any existing machinelearning functionals, predicting ground-state energies of test systems with amean absolute error of 2.7 milli-Hartrees.

How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?