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Machine learning Calabi-Yau four-folds

He, Y. ORCID: 0000-0002-0787-8380 and 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.

Publication Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 23 Apr 2021 13:07
URI: https://openaccess.city.ac.uk/id/eprint/25967
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