Complete and Efficient Covariants for 3D Point Configurations with Application to Learning Molecular Quantum Properties
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910589202202624 |
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| author | Maennel, Hartmut Unke, Oliver T. Müller, Klaus-Robert |
| author_facet | Maennel, Hartmut Unke, Oliver T. Müller, Klaus-Robert |
| contents | When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness properties for higher order methods, and show that $6k-5$ of these features are enough for up to $k$ atoms. We also find that the Clebsch--Gordan operations commonly used in these methods can be replaced by matrix multiplications without sacrificing completeness, lowering the scaling from $O(l^6)$ to $O(l^3)$ in the degree of the features. We apply this to quantum chemistry, but the proposed methods are generally applicable for problems involving 3D point configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete and Efficient Covariants for 3D Point Configurations with Application to Learning Molecular Quantum Properties Maennel, Hartmut Unke, Oliver T. Müller, Klaus-Robert Machine Learning Chemical Physics When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness properties for higher order methods, and show that $6k-5$ of these features are enough for up to $k$ atoms. We also find that the Clebsch--Gordan operations commonly used in these methods can be replaced by matrix multiplications without sacrificing completeness, lowering the scaling from $O(l^6)$ to $O(l^3)$ in the degree of the features. We apply this to quantum chemistry, but the proposed methods are generally applicable for problems involving 3D point configurations. |
| title | Complete and Efficient Covariants for 3D Point Configurations with Application to Learning Molecular Quantum Properties |
| topic | Machine Learning Chemical Physics |
| url | https://arxiv.org/abs/2409.02730 |