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

2020/09/30 by Li Li, Stephan Hoyer, Ryan Pederson +4 · 1 citation
Physics and Astronomy · Computer Science · #physics.comp-ph #cs.LG

paper · pdf · doi:10.1103/physrevlett.126.036401

published as Phys. Rev. Lett. 126, 036401 (2021)

arxiv created 2020/11/17 · arxiv updated 2021/01/25

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 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 H₂ dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.

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