Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912101405032448 |
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| author | Zaverkin, Viktor Alesiani, Francesco Maruyama, Takashi Errica, Federico Christiansen, Henrik Takamoto, Makoto Weber, Nicolas Niepert, Mathias |
| author_facet | Zaverkin, Viktor Alesiani, Francesco Maruyama, Takashi Errica, Federico Christiansen, Henrik Takamoto, Makoto Weber, Nicolas Niepert, Mathias |
| contents | The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_14253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing Zaverkin, Viktor Alesiani, Francesco Maruyama, Takashi Errica, Federico Christiansen, Henrik Takamoto, Makoto Weber, Nicolas Niepert, Mathias Machine Learning Computational Physics The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models. |
| title | Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing |
| topic | Machine Learning Computational Physics |
| url | https://arxiv.org/abs/2405.14253 |