Self-consistent electron density with shell structure using neural network-based Pauli potential.

This article focuses on developing a feed-forward neural network (NN) model to represent the Pauli potential—an unknown component of the kinetic energy functional—in orbital-free density functional theory (OF-DFT) for atomic systems with spherically symmetric ground-state electron densities. Using electron density grids as input, the NN predicts the Pauli potential, which, combined with the Hohenberg–Kohn variational principle, enables accurate self-consistent calculation of radial electron densities that reproduce atomic shell structures. The study demonstrates high accuracy for smaller atoms and reasonable predictions for larger atoms, including successful tests on atoms outside the training set. Additionally, the NN-based Pauli potential allows calculation of the non-interacting kinetic energy without functional derivatives, marking a significant advancement in applying machine learning to improve the efficiency and accuracy of OF-DFT electronic structure calculations.