Machine learning Calabi-Yau four-folds

He, Y. ORCID: 0000-0002-0787-8380 & Lukas, A. (2021). Machine learning Calabi-Yau four-folds. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 815, 136139. doi: 10.1016/j.physletb.2021.136139

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 and h for these manifolds. We find that h can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h , we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h , at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.