# Constructing and Machine Learning Calabi-Yau Five-folds

arXiv: https://arxiv.org/abs/2310.15966 · HTML: https://mlsanity.com/paper/2310.15966/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 75 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Machine learning Calabi-Yau metrics](https://mlsanity.com/paper/1910.08605/) (2019)
- [Machine Learning CICY Threefolds](https://mlsanity.com/paper/1806.03121/) (2018)
- [The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning](https://mlsanity.com/paper/1812.02893/) (2018)
- [Machine learning for complete intersection Calabi-Yau manifolds: a methodological study](https://mlsanity.com/paper/2007.15706/) (2020)
- [Machine Learning Calabi-Yau Four-folds](https://mlsanity.com/paper/2009.02544/) (2020)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Inception Neural Network for Complete Intersection Calabi-Yau 3-folds](https://mlsanity.com/paper/2007.13379/) (2020)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Heterotic String Model Building with Monad Bundles and Reinforcement Learning](https://mlsanity.com/paper/2108.07316/) (2021)

## Built on by (most cited first, 4 of 4)

- [Machine Learning Toric Duality in Brane Tilings](https://mlsanity.com/paper/2409.15251/) (2024)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)

## Abstract (arXiv)

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 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. For h1,4,h2,3, η, we also find very high R2 scores, but the accuracy is lower, due to the large ranges of possible values.