Generalizability of density functionals learned from differentiable programming on weakly correlated spin-polarized 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 framework. We evaluate the generalizability of KSR by training on atomic systems and testing on molecules at equilibrium. We propose a spin-polarized version of KSR with local, semilocal, and nonlocal approximations for the exchange-correlation functional. 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.

Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics

Including prior knowledge is important for effective machine learning models in physics, and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H$_2$ dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.