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DeepH-GW is an equivariant message-passing neural network framework that directly predicts effective $GW$ quasiparticle Hamiltonians from atomic structures, bypassing the prohibitive computational scaling of first-principles excited-state calculations. By coupling high-fidelity plane-wave $GW$ calculations to a real-space Hamiltonian reconstruction interface, the approach achieves linear-scaling inference for many-body electronic structures. The model attains meV-level accuracy across quasiparticle band structures and transfers robustly from small training cells to large supercells, accurately capturing complex phenomena like electron-phonon band-gap renormalization.
Equivariant neural networks can bypass the brutal scaling of many-body $GW$ perturbation theory, achieving few-meV quasiparticle accuracy and cross-scale transferability at linear cost.
Accurate quasiparticle electronic structures are the foundation for understanding excited-state properties of materials and explaining optoelectronic, quantum, and transport phenomena. First-principles GW calculations nevertheless remain computationally intensive for large or configurationally complex systems. Here we introduce DeepH-GW, a deep-learning framework that predicts an effective GW quasiparticle Hamiltonian directly from atomic structure. Building on the local, equivariant message-passing architecture of DeepH, DeepH-GW is trained on high-fidelity plane-wave GW calculations through a real-space Hamiltonian-reconstruction interface. This approach combines the systematic accuracy and broad chemical applicability of plane-wave methods with linear-scaling neural-network inference. Across the systems examined, DeepH-GW reproduces quasiparticle band structures with errors on the order of a few meV. Moreover, we show that, despite the intrinsic nonlocality of many-body interactions, DeepH-GW exhibits strong cross-scale transferability from relatively small training structures to substantially larger supercells. We demonstrate that the framework can accurately capture GW-level electron-phonon band-gap renormalization through predictions in supercells with thermal displacements, illustrating the power of the approach. DeepH-GW therefore provides a practical route toward large-scale many-body simulations and foundation models for excited-state electronic structure.