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

TL;DR

This paper demonstrates that incorporating the Kohn-Sham equations as a regularizer during neural network training for exchange-correlation functionals significantly enhances model generalization, accuracy, and ability to handle strongly correlated systems in physics.

Contribution

It introduces a novel approach of embedding the Kohn-Sham equations into neural network training as an implicit regularizer, improving physics-based machine learning models.

Findings

Achieves chemical accuracy for H2 dissociation curve with minimal separations.

Models generalize well to unseen molecules and reduce self-interaction error.

Implicit regularization via Kohn-Sham equations enhances model performance.

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 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.