In recent years, the intersection of machine learning and geometry has seen significant advancements, yet directly predicting geometric quantities remains a challenge. This research investigates the application of convolutional neural networks (CNNs) for predicting intersection numbers within the framework of twisted Complete Intersection Calabi-Yau (CICY) manifolds, effectively distinguishing between different topological classes. Our proposed CNN competently models complex spatial relationships in configuration matrices and twistness quantities. The network achieves an accuracy of 0.7647 for \(d_2\) and 0.7941 for \(d_3\) on 10% validation, consistently outperforming alternative methods such as XGBoost, Random Forest, and Logistic Regression across varying validation splits. These results underscore CNNs’ capability to capture spatial relationships and provide a robust tool for topological classification. Future work will focus on addressing class imbalance and exploring geometric indices in broader contexts, offering new insights into compactification scenarios and index theory.

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Topological Classification of Twisted CICY Using Convolutional Neural Network

  • Song Xu

摘要

In recent years, the intersection of machine learning and geometry has seen significant advancements, yet directly predicting geometric quantities remains a challenge. This research investigates the application of convolutional neural networks (CNNs) for predicting intersection numbers within the framework of twisted Complete Intersection Calabi-Yau (CICY) manifolds, effectively distinguishing between different topological classes. Our proposed CNN competently models complex spatial relationships in configuration matrices and twistness quantities. The network achieves an accuracy of 0.7647 for \(d_2\) and 0.7941 for \(d_3\) on 10% validation, consistently outperforming alternative methods such as XGBoost, Random Forest, and Logistic Regression across varying validation splits. These results underscore CNNs’ capability to capture spatial relationships and provide a robust tool for topological classification. Future work will focus on addressing class imbalance and exploring geometric indices in broader contexts, offering new insights into compactification scenarios and index theory.