General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian

• Published in: Nature communications Vol. 14; no. 1; pp. 2848 - 10
• Main Authors: Gong, Xiaoxun, Li, He, Zou, Nianlong, Xu, Runzhang, Duan, Wenhui, Xu, Yong
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 18.05.2023; Nature Publishing Group; Nature Portfolio
• Subjects: 639/301/1034/1037; 639/301/1034/1038; 639/705/117; 639/766/119/995; Accuracy; Deep learning; Density functional theory; Electronic structure; Hamiltonian functions; Humanities and Social Sciences; multidisciplinary; Neural networks; Science; Science (multidisciplinary); Spin-orbit interactions; Structure-function relationships; Symmetry
• DOI: 10.1038/s41467-023-38468-8
• ISSN: 2041-1723

The 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 efficient electronic structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making the routine study of large-scale supercells (>10 4 atoms) feasible. 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 opportunities for materials research, such as building a Moiré-twisted material database. Fundamental symmetries are crucial to the deep-learning modeling of physical systems. Here the authors use equivariant neural networks preserving the Euclidean symmetries to accelerate electronic structure calculations by orders of magnitude keeping sub-meV accuracy.