Combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling. Our DeepH-E3 method enables very efficient electronic-structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making routine study of large-scale supercells (>104 atoms) feasible. Remarkably, the method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development, but also creates new opportunities for materials research, such as building Moir\'e-twisted material database.
@article{arxiv.2210.13955,
title = {General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian},
author = {Xiaoxun Gong and He Li and Nianlong Zou and Runzhang Xu and Wenhui Duan and Yong Xu},
journal= {arXiv preprint arXiv:2210.13955},
year = {2023}
}