Deep learning density functionals for gradient descent optimization

TL;DR

This paper introduces a convolutional neural network architecture with an inter-channel averaging layer to improve the stability and accuracy of density functional derivatives in quantum many-body problems, enabling reliable gradient descent optimization.

Contribution

It proposes a novel neural network design that reduces noise in functional derivatives, enhancing the stability of density functional theory calculations.

Findings

Stable gradient-based optimization achieved for noninteracting atoms in optical speckle disorder.

Accurate ground-state energies and densities obtained without instabilities.

Systematic improvement of results demonstrated with the new architecture.

Abstract

Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily be trained to accurately map ground-state density profiles to the corresponding energies, their functional derivatives often turn out to be too noisy, leading to instabilities in self-consistent iterations and in gradient-based searches of the ground-state density profile. We investigate how these instabilities occur when standard deep neural networks are adopted as regression models, and we show how to avoid it using an ad-hoc convolutional architecture featuring an inter-channel averaging layer. The testbed we consider is a realistic model for noninteracting atoms in optical speckle disorder. With the inter-channel average, accurate and systematically improvable ground-state energies and density profiles are obtained via gradient-descent optimization, without instabilities nor violations of the variational principle.