Machine learning Calabi-Yau four-folds

Machine learning Calabi-Yau four-folds

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 super...

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Main Authors: Yang-Hui He, Andre Lukas
Format: Article
Language:English
Published: Elsevier 2021-04-01
Series:Physics Letters B
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269321000794
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spelling doaj-e672856772ac4114b3391d12e3966d232021-03-22T12:35:23ZengElsevierPhysics Letters B0370-26932021-04-01815136139Machine learning Calabi-Yau four-foldsYang-Hui He0Andre Lukas1Department of Mathematics, City, University of London, London EC1V 0HB, UK; Merton College, University of Oxford, OX1 4JD, UK; School of Physics, NanKai University, Tianjin, 300071, PR China; Corresponding author.Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UKHodge 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 h1,1 and h3,1 for these manifolds. We find that h1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.http://www.sciencedirect.com/science/article/pii/S0370269321000794
collection DOAJ
language English
format Article
sources DOAJ
author Yang-Hui He
Andre Lukas
spellingShingle Yang-Hui He
Andre Lukas
Machine learning Calabi-Yau four-folds
Physics Letters B
author_facet Yang-Hui He
Andre Lukas
author_sort Yang-Hui He
title Machine learning Calabi-Yau four-folds
title_short Machine learning Calabi-Yau four-folds
title_full Machine learning Calabi-Yau four-folds
title_fullStr Machine learning Calabi-Yau four-folds
title_full_unstemmed Machine learning Calabi-Yau four-folds
title_sort machine learning calabi-yau four-folds
publisher Elsevier
series Physics Letters B
issn 0370-2693
publishDate 2021-04-01
description 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 h1,1 and h3,1 for these manifolds. We find that h1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.
url http://www.sciencedirect.com/science/article/pii/S0370269321000794
work_keys_str_mv AT yanghuihe machinelearningcalabiyaufourfolds
AT andrelukas machinelearningcalabiyaufourfolds
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