## 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

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BibTeX]

*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

**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.

**Tags:**
PRIN2022-MFDS