Machine Learning CICY Threefolds

TL;DR

This paper applies neural networks and SVMs to predict geometric properties of CICY threefolds, significantly improving accuracy and enabling quick screening of string models in algebraic geometry.

Contribution

It introduces machine learning techniques to accurately predict Hodge numbers, favorability, and symmetries of CICY threefolds, advancing computational methods in algebraic geometry.

Findings

Improved prediction of Hodge numbers over previous methods

Effective handling of class imbalance with SMOTE and permutations

Fast diagnostic tools for shortlisting string models

Abstract

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.