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

Xiaoxun Gong, He Li, Nianlong Zou, Runzhang Xu, Wenhui Duan () and Yong Xu ()
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Xiaoxun Gong: Tsinghua University
He Li: Tsinghua University
Nianlong Zou: Tsinghua University
Runzhang Xu: Tsinghua University
Wenhui Duan: Tsinghua University
Yong Xu: Tsinghua University

Nature Communications, 2023, vol. 14, issue 1, 1-10

Abstract: Abstract 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 (>104 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.

Date: 2023
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DOI: 10.1038/s41467-023-38468-8

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