Distinguishing Calabi-Yau Topology using Machine Learning

TL;DR

This paper demonstrates that machine learning, specifically Inception CNNs, can accurately predict the topology of Calabi-Yau manifolds based on their intersection numbers, advancing computational methods in algebraic geometry.

Contribution

It introduces a machine learning approach to classify Calabi-Yau topologies using triple intersection numbers, achieving high accuracy and extending AI applications in pure mathematics.

Findings

Achieved approximately 90% accuracy in predicting Calabi-Yau topology.

Validated the effectiveness of CNNs in algebraic geometry classification tasks.

Showed potential for machine learning to identify complex manifold invariants.

Abstract

While the earliest applications of AI methodologies to pure mathematics and theoretical physics began with the study of Hodge numbers of Calabi-Yau manifolds, the topology type of such manifold also crucially depend on their intersection theory. Continuing the paradigm of machine learning algebraic geometry, we here investigate the triple intersection numbers, focusing on certain divisibility invariants constructed therefrom, using the Inception convolutional neural network. We find $\sim90\%$ accuracies in prediction in a standard fivefold cross-validation, signifying that more sophisticated tasks of identification of manifold topologies can also be performed by machine learning.