Machine Learning Calabi-Yau Three-Folds, Four-Folds, and Five-Folds

Abstract

In this manuscript, we demonstrate, using several regression techniques, that the remaining independent Hodge numbers of complete intersection Calabi-Yau four-folds and five-folds can be machine learned from $h^{1,1}$ and $h^{2,1}$. Consequently, we combine the Hodge numbers $h^{1,1}$ and $h^{2,1}$ from the complete intersection Calabi-Yau three-folds, four-folds, and five-folds into a single dataset. We then implement various classification algorithms on this dataset. For example, Gaussian process and naive Bayes classifiers both achieve $100\%$ accuracy in binary classification between three-folds and four-folds. Using the Support Vector Machine (SVM) algorithm, a special corner is identified in the Calabi-Yau four-fold landscape (characterized by $15 \leq h^{1,1} \leq 30$ and $95 \leq h^{2,1} \leq 100$) during multiclass classification. Furthermore, the highest accuracy $1.00000$, in classifying Calabi-Yau three-folds, four-folds, and five-folds is obtained using the naive Bayes classifier.