Deep-learning density functionals for gradient descent optimization.

Area of Science:

• Computational Physics
• Quantum Mechanics
• Machine Learning

Background:

• Machine-learned regression models offer efficient solutions for energy-density functionals in quantum many-body problems.
• Accurate mapping of ground-state density profiles to energies is achievable, but functional derivatives often exhibit noise, causing instabilities in calculations.

Purpose of the Study:

• To investigate the causes of instabilities in machine-learned energy-density functionals using standard deep neural networks.
• To develop and validate a novel convolutional architecture that mitigates these instabilities.

Main Methods:

• Utilized a custom convolutional neural network architecture incorporating an interchannel averaging layer.
• Tested the model on a realistic system of noninteracting atoms in optical speckle disorder.
• Employed gradient-descent optimization for ground-state density profile searches.

Main Results:

• The ad hoc convolutional architecture effectively suppressed noise in functional derivatives, preventing instabilities.
• Achieved accurate and systematically improvable ground-state energies and density profiles.
• Demonstrated the avoidance of variational principle violations during optimization.

Conclusions:

• A convolutional architecture with interchannel averaging provides a stable and accurate method for machine-learned energy-density functionals.
• This approach enhances the reliability of density functional theory calculations for quantum many-body systems.