Accelerating electronic structure calculations using an E(3)-equivariant neural network

The combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research. However, designing neural network models that effectively incorporate symmetry requirements and a priori knowledge of physical systems remains a significant challenge. Here, we present an E(3)-equivariant deep-learning framework that models the density functional theory (DFT) Hamiltonian as a function of material structure [1, 2]. The neural network respects the Euclidean symmetry of material systems and leverages the locality property of electronic matter, allowing us to achieve sub-meV level accuracy in electronic structure calculations with small-sized training structures [1-3]. Our method scales linearly with system size and is applicable to materials with up to 10⁴ atoms. Additionally, our method can be integrated with advanced computational techniques beyond the DFT level, such as hybrid functionals [4]. This not only advances the field of deep-learning method development but also opens new possibilities for materials research.