Search for Z/2 eigenfunctions on the sphere using machine learning
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918096215736320 |
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| author | Haydys, Andriy Salm, Willem Adriaan |
| author_facet | Haydys, Andriy Salm, Willem Adriaan |
| contents | We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we implemented it using the JAX library. We found Z/2 eigenfunctions for three cases: In the first two cases we fixed the branch points at the vertices of a tetrahedron and at a cube respectively. In a third case, we allowed the AI to move the branch points around and, in the end, it positioned the branch points at the vertices of a squashed tetrahedron. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Search for Z/2 eigenfunctions on the sphere using machine learning Haydys, Andriy Salm, Willem Adriaan Differential Geometry Machine Learning Numerical Analysis 53-08, 53C99 We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we implemented it using the JAX library. We found Z/2 eigenfunctions for three cases: In the first two cases we fixed the branch points at the vertices of a tetrahedron and at a cube respectively. In a third case, we allowed the AI to move the branch points around and, in the end, it positioned the branch points at the vertices of a squashed tetrahedron. |
| title | Search for Z/2 eigenfunctions on the sphere using machine learning |
| topic | Differential Geometry Machine Learning Numerical Analysis 53-08, 53C99 |
| url | https://arxiv.org/abs/2507.13122 |