Generalizable machine-learned density functionals using a spin-adapted Kohn-Sham regularizer*

The generalization performance of an exchange-correlation (XC) functional approximation largely determines its practical usefulness in density functional theory (DFT) calculations. For training machine-learned XC functional models, the Kohn-Sham regularizer (KSR) method has been shown to greatly improve generalization [1]. To extend this approach, we propose a spin-adapted version of KSR with local, semilocal, and nonlocal neural network model approximations for the XC energy functional. Using 1-dimensional (1D) analog model systems, we assess generalizability by training on a handful of 1D atomic systems and testing on a set of 1D equilibrium-bonded molecules. The performance of the various trained neural XC models is analyzed. In particular, we find that our nonlocal XC model obtains near chemical accuracy for ground-state properties of 1D molecules in the test set.

[1] Li, Li, et al. "Kohn-Sham equations as regularizer: Building prior knowledge into machine-learned physics." Physical review letters 126.3 (2021): 036401.