Constructing and Machine Learning Calabi-Yau Five-folds

• URL: http://arxiv.org/abs/2310.15966v2
• Date: Tue, 9 Jan 2024 19:00:00 GMT
• Title: Constructing and Machine Learning Calabi-Yau Five-folds
• Authors: R. Alawadhi, D. Angella, A. Leonardo and T. Schettini Gherardini
• Abstract summary: Supervised machine learning is performed on the cohomological data. We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces. We find that $h1,1$ can be learnt very efficiently, with very high $R2$ score and an accuracy of $96%$, i.e. $96 %$ of the predictions exactly match the correct values.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $h^{1,4},h^{2,3}, \eta$, we also find very high $R^2$ scores, but the accuracy is lower, due to the large ranges of possible values.

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