Towards Harmonization of SO(3)-Equivariance and Expressiveness: a Hybrid Deep Learning Framework for Electronic-Structure Hamiltonian Prediction
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911929070518272 |
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| author | Yin, Shi Pan, Xinyang Zhu, Xudong Gao, Tianyu Zhang, Haochong Wu, Feng He, Lixin |
| author_facet | Yin, Shi Pan, Xinyang Zhu, Xudong Gao, Tianyu Zhang, Haochong Wu, Feng He, Lixin |
| contents | Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks remains unsolved. To navigate the harmonization between equivariance and expressiveness, we propose a deep learning method synergizing two distinct categories of neural mechanisms as a two-stage encoding and regression framework. The first stage corresponds to group theory-based neural mechanisms with inherent SO(3)-equivariant properties prior to the parameter learning process, while the second stage is characterized by a non-linear 3D graph Transformer network we propose, featuring high capability on non-linear expressiveness. The novel combination lies in the point that, the first stage predicts baseline Hamiltonians with abundant SO(3)-equivariant features extracted, assisting the second stage in empirical learning of equivariance; and in turn, the second stage refines the first stage's output as a fine-grained prediction of Hamiltonians using powerful non-linear neural mappings, compensating for the intrinsic weakness on non-linear expressiveness capability of mechanisms in the first stage. Our method enables precise, generalizable predictions while capturing SO(3)-equivariance under rotational transformations, and achieves state-of-the-art performance in Hamiltonian prediction on six benchmark databases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards Harmonization of SO(3)-Equivariance and Expressiveness: a Hybrid Deep Learning Framework for Electronic-Structure Hamiltonian Prediction Yin, Shi Pan, Xinyang Zhu, Xudong Gao, Tianyu Zhang, Haochong Wu, Feng He, Lixin Computational Physics Materials Science Machine Learning Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks remains unsolved. To navigate the harmonization between equivariance and expressiveness, we propose a deep learning method synergizing two distinct categories of neural mechanisms as a two-stage encoding and regression framework. The first stage corresponds to group theory-based neural mechanisms with inherent SO(3)-equivariant properties prior to the parameter learning process, while the second stage is characterized by a non-linear 3D graph Transformer network we propose, featuring high capability on non-linear expressiveness. The novel combination lies in the point that, the first stage predicts baseline Hamiltonians with abundant SO(3)-equivariant features extracted, assisting the second stage in empirical learning of equivariance; and in turn, the second stage refines the first stage's output as a fine-grained prediction of Hamiltonians using powerful non-linear neural mappings, compensating for the intrinsic weakness on non-linear expressiveness capability of mechanisms in the first stage. Our method enables precise, generalizable predictions while capturing SO(3)-equivariance under rotational transformations, and achieves state-of-the-art performance in Hamiltonian prediction on six benchmark databases. |
| title | Towards Harmonization of SO(3)-Equivariance and Expressiveness: a Hybrid Deep Learning Framework for Electronic-Structure Hamiltonian Prediction |
| topic | Computational Physics Materials Science Machine Learning |
| url | https://arxiv.org/abs/2401.00744 |