Y. He

S. Yao

S. T. Yau

Using Inception, a convolutional neural network, we predict certain divisibility invariants of Calabi-Yau manifolds with up to 90% accuracy.

While early experiments in AI for mathematics and theoretical physics aimed to predict the Hodge numbers of Calabi-Yau manifolds, more refined invariants in their intersection theory – specifically, their triple intersection numbers and divisibility invariants – are needed to fully characterise their topology. Here, these invariants are predicted with around 90% accuracy using an Inception convolutional neural network.

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 ∼90% 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.

Convolution in topology

Distinguishing Calabi-Yau topology using machine learning