Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
This addresses the challenge of building effective machine learning models in physics by leveraging embedded computational priors, though it is incremental in applying known equations to a specific domain.
The paper tackled the problem of incorporating prior knowledge into machine learning models for physics by using the Kohn-Sham equations as an implicit regularizer during training, resulting in learning the entire H2 dissociation curve within chemical accuracy with only two separations and generalizing to unseen molecules.
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.