Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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R. Alawadhi - D. Angella - A. Leonardo - T. Schettini Gherardini

Constructing and Machine Learning Calabi-Yau Five-folds

created by daniele on 25 Oct 2023
modified on 09 Feb 2024


Published Paper

Inserted: 25 oct 2023
Last Updated: 9 feb 2024

Journal: Fortschr. Phys.
Volume: 72
Number: 2
Pages: 2300262
Year: 2024
Doi: 10.1002/prop.202300262

ArXiv: 2310.15966 PDF


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.comsclfoz7ii5idt6qxu36e0b8azqh?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.

Tags: PRIN2022-MFDS

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