Machine learning Calabi-Yau hypersurfaces

Abstract

We revisit the classic database of weighted-${\mathbb{P}}^{4}\mathrm{s}$ which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of ${R}^{2}>95%$. Supervised learning also allows us to identify weighted-${\mathbb{P}}^{4}\mathrm{s}$ which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behavior.