Machine Learning Calabi-Yau Hypersurfaces

TL;DR

This paper applies machine learning methods to analyze Calabi-Yau hypersurfaces in weighted projective 4-spaces, revealing new patterns and enabling highly accurate predictions of topological properties from weights.

Contribution

It introduces the use of unsupervised and supervised machine learning techniques to uncover hidden structures and predict topological data of Calabi-Yau hypersurfaces, a novel approach in this context.

Findings

Uncovered an almost linear dependence of topological data on weights.

Identified previously unnoticed clustering in Calabi-Yau data.

Achieved over 95% accuracy in predicting topological parameters from weights.

Abstract

We revisit the classic database of weighted-P4s 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-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.