Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds

TL;DR

This paper explores using neural networks to classify and generate generalized Complete Intersection Calabi-Yau manifolds, significantly improving efficiency and accuracy in a complex mathematical classification task.

Contribution

It introduces a machine learning approach to classify and predict new gCICYs, demonstrating high precision and potential to accelerate research in this complex area.

Findings

High accuracy on existing gCICY types

97% precision in predicting new gCICYs

Machine learning effectively classifies complex geometric structures

Abstract

Generalized Complete Intersection Calabi-Yau Manifold (gCICY) is a new construction of Calabi-Yau manifolds established recently. However, the generation of new gCICYs using standard algebraic method is very laborious. Due to this complexity, the number of gCICYs and their classification still remain unknown. In this paper, we try to make some progress in this direction using neural network. The results showed that our trained models can have a high precision on the existing type $(1,1)$ and type $(2,1)$ gCICYs in the literature. Moreover, They can achieve a $97\%$ precision in predicting new gCICY which is generated differently from those used for training and testing. This shows that machine learning could be an effective method to classify and generate new gCICY.