Flexible SE(2) graph neural networks with applications to PDE surrogates
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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_ | 1866909213419110400 |
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| author | Bånkestad, Maria Mogren, Olof Pirinen, Aleksis |
| author_facet | Bånkestad, Maria Mogren, Olof Pirinen, Aleksis |
| contents | This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flexible SE(2) graph neural networks with applications to PDE surrogates Bånkestad, Maria Mogren, Olof Pirinen, Aleksis Machine Learning Artificial Intelligence Numerical Analysis Fluid Dynamics This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy. |
| title | Flexible SE(2) graph neural networks with applications to PDE surrogates |
| topic | Machine Learning Artificial Intelligence Numerical Analysis Fluid Dynamics |
| url | https://arxiv.org/abs/2405.20287 |