Machine Learning Calabi-Yau Four-folds

Abstract

Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h^1,1 and h^3,1 for these manifolds. We find that h^1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h^3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.

6 pages, 2 figures; references added

References in corpus (4)

• Heterotic Compactification, An Algorithmic Approach
• Machine Learning of Calabi-Yau Volumes
• Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
• Getting CICY High

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