Transformer-inspired architectures make machine-learned electron densities accurate and transferable enough to bypass self-consistency

Abstract

We introduce machine learning models that accurately predict the electron density, the central variable of density functional theory. They are built on Transformer-inspired architectures, which require little computation per parameter and can therefore be enlarged at low cost. The proposed models, SwinUNETR-V2 and its attention-free counterpart NeXtUNETR, achieve state-of-the-art accuracy on QM9, with normalized mean absolute errors in the density averaging 0.075% and 0.046%, respectively. The predicted densities are accurate enough to bypass the self-consistent iteration: a single Kohn-Sham step reproduces the self-consistent electronic structure. For NeXtUNETR, the median errors are 0.036 meV in the total energy, 0.65 meV/angstrom in the forces and 1.8 meV in the HOMO-LUMO gap. The forces not only recover the self-consistent minima in geometry optimization but also successfully drive ab initio molecular dynamics. Fine-tuned on small datasets, both networks also transfer accurately to systems containing elements absent from QM9 or larger than its molecules.