Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics.

Area of Science:

• Computational physics
• Quantum chemistry
• Machine learning

Background:

• Prior knowledge integration is crucial for effective machine learning in physics.
• Current methods often involve explicit loss terms or architectural constraints.
• Embedding physics within the computation itself is an underutilized approach.

Purpose of the Study:

• To demonstrate the benefits of implicit physics regularization in neural network training.
• To investigate the use of Kohn-Sham equation solutions for learning quantum mechanical functionals.
• To improve the generalization and accuracy of machine learning models for electronic structure calculations.

Main Methods:

• Training neural networks to learn the exchange-correlation functional by solving Kohn-Sham equations.
• Utilizing two specific separations to model the H2 dissociation curve.
• Evaluating model performance on one-dimensional molecular systems.

Main Results:

• Implicit regularization via Kohn-Sham solvers significantly enhances model generalization.
• Achieved chemical accuracy for the entire one-dimensional H2 dissociation curve, including strongly correlated regions.
• Demonstrated generalization to unseen molecules and mitigation of self-interaction error.

Conclusions:

• Solving Kohn-Sham equations during neural network training offers powerful implicit regularization for physics-informed machine learning.
• This approach enables accurate and generalizable models for quantum chemistry, overcoming limitations of traditional methods.
• The method shows promise for advancing computational materials science and drug discovery through more efficient and accurate simulations.