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

Abstract: In this manuscript, we demonstrate, by using several regression techniques, that one can machine learn the other independent Hodge numbers of complete intersection Calabi-Yau four-folds and five-folds in terms of $h^{1,1}$ and $h^{2,1}$. Consequently, we combine the Hodge numbers $h^{1,1}$ and $h^{2,1}$ from the complete intersection of Calabi-Yau three-folds, four-folds, and five-folds into a single dataset. We then implemented various classification algorithms on this dataset. For example, the accuracy of the Gaussian process and the naive Bayes classifications are all $100\%$ when a binary classification of three-folds and four-folds is performed. With the Support Vector Machine (SVM) algorithm plots, a special corner is detected in the Calabi-Yau three-folds landscape (characterized by $17\leq h^{1,1}\leq 30$ and $20\leq h^{2,1}\leq 40$) when multiclass classification is performed. Furthermore, the best accuracy, $0.996459$, in classifying Calabi-Yau three-folds, four-folds, and five-folds, is obtained with the naive Bayes classification.