Machine Learning Calabi-Yau Hypersurfaces
This work provides incremental improvements in applying machine learning to mathematical physics, specifically for classifying and predicting properties of Calabi-Yau manifolds.
The authors tackled the problem of analyzing Calabi-Yau 3-fold hypersurfaces from a database of weighted-P4s using machine learning, achieving over 95% accuracy in predicting topological parameters and 100% accuracy in identifying admissible hypersurfaces.
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.