Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds

Aggarwal, Daattavya; He, Yang-Hui; Heyes, Elli; Hirst, Edward; Sá Earp, Henrique N.; Silva, Tomás S.R.

doi:10.1016/j.physletb.2024.138517

Physics Letters B

2024

DOI: 10.1016/j.physletb.2024.138517

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Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds

Daattavya Aggarwal,

Yang-Hui He,

Elli Heyes

et al.

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2024

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Cited by 2 publications

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Calabi-Yau four-, five-, sixfolds as Pwn hypersurfaces: Machine learning, approximation, and generation

Hirst,

Gherardini

2024

Phys. Rev. D

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Calabi-Yau fourfolds may be constructed as hypersurfaces in weighted projective spaces of complex dimension five defined via weight systems of six weights. In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers from the weight systems, where gradient saliency and symbolic regression then inspired a truncation of the Landau-Ginzburg model formula for the Hodge numbers of any dimensional Calabi-Yau constructed in this way. The approximation always provides a tight lower bound, is shown to be dramatically quicker to compute (with computation times reduced by up to 4 orders of magnitude), and gives remarkably accurate results for systems with large weights. Additionally, complementary datasets of weight systems satisfying the necessary but insufficient conditions for transversality were constructed, including considerations of the interior point, reflexivity, and intradivisibility properties, overall producing a classification of this weight system landscape, further confirmed with machine learning methods. Using the knowledge of this classification and the properties of the presented approximation, a novel dataset of transverse weight systems consisting of seven weights was generated for a sum of weights ≤200, producing a new database of Calabi-Yau fivefolds, with their respective topological properties computed. Furthermore, an equivalent database of candidate Calabi-Yau sixfolds was generated with approximated Hodge numbers. Published by the American Physical Society 2024

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Calabi-Yau four-, five-, sixfolds as Pwn hypersurfaces: Machine learning, approximation, and generation

Hirst,

Gherardini

2024

Phys. Rev. D

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Machine learning complete intersection Calabi-Yau 3-folds

Keita

2024

Phys. Rev. D

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Gaussian process regression, kernel support vector regression, the random forest, extreme gradient boosting, and the generalized linear model algorithms are applied to data of complete intersection Calabi-Yau threefolds. It is shown that Gaussian process regression is the most suitable for learning the Hodge number h2,1 in terms of h1,1. The performance of this regression algorithm is such that the Pearson correlation coefficient for the validation set is R2=0.9999999995 with a root mean square error RMSE=0.0002895011. As for the train set, these two parameters are as follows: R2=0.9999999994 and RMSE=0.0002854348. The training error and the cross-validation error of this regression are 1×10−9 and 1.28×10−7, respectively. Learning the Hodge number h1,1 in terms of h2,1 yields R2=1.000000 and RMSE=7.395731×10−5 for the validation set of the Gaussian process regression. Published by the American Physical Society 2024

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Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds

Cited by 2 publications

References 46 publications

Calabi-Yau four-, five-, sixfolds as Pwn hypersurfaces: Machine learning, approximation, and generation

Calabi-Yau four-, five-, sixfolds as Pwn hypersurfaces: Machine learning, approximation, and generation

Machine learning complete intersection Calabi-Yau 3-folds

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