2021/12/31 by David S. Berman, Yang-Hui He, Yang‐Hui He +1
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry and Number Theory #Algorithm #Artificial intelligence #Artificial neural network #Calabi–Yau manifold #Cluster analysis #Computer science #Hypersurface #Machine learning #Mathematics #Pure mathematics #Set (abstract data type) #Supervised learning #Toolbox #Topological and Geometric Data Analysis #Topological data analysis #Unsupervised learning #hep-th #math.AG #stat.ML
paper · pdf · doi:10.1103/physrevd.105.066002
32 pages, 43 figures
arxiv created 2022/01/19 · openalex publication_date 2022/03/09 · arxiv updated 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 R2 > 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.