Neural density functionals: Local learning and pair-correlation matching

TL;DR

This paper demonstrates that local learning of inhomogeneous one-body correlations enhances neural density functionals, with pair-correlation matching serving as an effective regularizer, leading to more flexible and accurate models beyond the training domain.

Contribution

It introduces local one-body learning for neural density functionals and advocates for pair-correlation matching as a regularizer, improving model flexibility and accuracy.

Findings

Local learning improves neural density functional accuracy.

Pair-correlation matching acts as an effective regularizer.

Convolutional neural networks can transcend training boundaries.

Abstract

Recently Dijkman et al. (arXiv:2403.15007) proposed training classical neural density functionals via bulk pair-correlation matching. We show their method to be an efficient regularizer for neural functionals based on local learning of inhomogeneous one-body direct correlations [Samm\"uller et al., Proc. Natl. Acad. Sci. 120, e2312484120 (2023), 10.1073/pnas.2312484120]. While Dijkman et al. demonstrated pair-correlation matching of a global neural free energy functional, we argue in favor of local one-body learning for flexible neural modelling of the full Mermin-Evans density functional map. Using spatial localization gives access to accurate neural free energy functionals, including convolutional neural networks, that transcend the training box.