Recently, radical progress in machine learning (ML) has revolutionized computational materials science, enabling unprecedentedly rapid materials discovery and property prediction, but the quantum many-body problem -- which is the key to understanding excited-state properties, ranging from transport to optics -- remains challenging due to the complexity of the nonlocal and energy-dependent interactions. Here, we propose a symmetry-aware, grid-free, transformer-based model, MBFormer, that is designed to learn the entire many-body hierarchy directly from mean-field inputs, exploiting the attention mechanism to accurately capture many-body correlations between mean-field states. As proof of principle, we demonstrate the capability of MBFormer in predicting results based on the GW plus Bethe Salpeter equation (GW-BSE) formalism, including quasiparticle energies, exciton energies, exciton oscillator strengths, and exciton wavefunction distribution. Our model is trained on a dataset of 721 two-dimensional materials from the C2DB database, achieving state-of-the-art performance with a low prediction mean absolute error (MAE) on the order of 0.1-0.2 eV for state-level quasiparticle and exciton energies across different materials. Moreover, we show explicitly that the attention mechanism plays a crucial role in capturing many-body correlations. Our framework provides an end-to-end platform from ground states to general many-body prediction in real materials, which could serve as a foundation model for computational materials science.
@article{arxiv.2507.05480,
title = {MBFormer: A General Transformer-based Learning Paradigm for Many-body Interactions in Real Materials},
author = {Bowen Hou and Xian Xu and Jinyuan Wu and Diana Y. Qiu},
journal= {arXiv preprint arXiv:2507.05480},
year = {2025}
}