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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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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