Abstract

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 consider the Kohn-Sham self-consistent calculation as a differentiable program and show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Our results serve as proof of principle for rethinking computational physics in this emerging paradigm of scientific computing with enormous development in automatic differentiation libraries, hardware accelerators and deep learning.