Constructing and Machine Learning Calabi-Yau Five-folds
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910292478263296 |
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| author | Alawadhi, R. Angella, D. Leonardo, A. Gherardini, T. Schettini |
| author_facet | Alawadhi, R. Angella, D. Leonardo, A. Gherardini, T. Schettini |
| contents | We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces, with up to four constraints. We obtain $27068$ spaces, which are not related by permutations of rows and columns of the configuration matrix, and determine the Euler number for all of them. Excluding the $3909$ product manifolds among those, we calculate the cohomological data for $12433$ cases, i.e. $53.7 \%$ of the non-product spaces, obtaining $2375$ different Hodge diamonds. The dataset containing all the above information is available at https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0 . The distributions of the invariants are presented, and a comparison with the lower-dimensional analogues is discussed. Supervised machine learning is performed on the cohomological data, via classifier and regressor (both fully connected and convolutional) neural networks. We find that $h^{1,1}$ can be learnt very efficiently, with very high $R^2$ score and an accuracy of $96\%$, i.e. $96 \%$ of the predictions exactly match the correct values. For $h^{1,4},h^{2,3}, η$, we also find very high $R^2$ scores, but the accuracy is lower, due to the large ranges of possible values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_15966 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constructing and Machine Learning Calabi-Yau Five-folds Alawadhi, R. Angella, D. Leonardo, A. Gherardini, T. Schettini High Energy Physics - Theory Machine Learning Algebraic Geometry We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces, with up to four constraints. We obtain $27068$ spaces, which are not related by permutations of rows and columns of the configuration matrix, and determine the Euler number for all of them. Excluding the $3909$ product manifolds among those, we calculate the cohomological data for $12433$ cases, i.e. $53.7 \%$ of the non-product spaces, obtaining $2375$ different Hodge diamonds. The dataset containing all the above information is available at https://www.dropbox.com/scl/fo/z7ii5idt6qxu36e0b8azq/h?rlkey=0qfhx3tykytduobpld510gsfy&dl=0 . The distributions of the invariants are presented, and a comparison with the lower-dimensional analogues is discussed. Supervised machine learning is performed on the cohomological data, via classifier and regressor (both fully connected and convolutional) neural networks. We find that $h^{1,1}$ can be learnt very efficiently, with very high $R^2$ score and an accuracy of $96\%$, i.e. $96 \%$ of the predictions exactly match the correct values. For $h^{1,4},h^{2,3}, η$, we also find very high $R^2$ scores, but the accuracy is lower, due to the large ranges of possible values. |
| title | Constructing and Machine Learning Calabi-Yau Five-folds |
| topic | High Energy Physics - Theory Machine Learning Algebraic Geometry |
| url | https://arxiv.org/abs/2310.15966 |