Machine Learning CICY Threefolds

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.

arXiv comment22 pages, 10 figures. V2: Added new results of using permutations of the CICY matrix to reduce the class imbalance when predicting discrete symmetries. V3: Corrected typing errors in table 5

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• Highly Symmetric Quintic Quotients
• Discrete Symmetries of Complete Intersection Calabi-Yau Manifolds

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