Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds
We propose a machine learning approach to study topological quantities related to the Sasakian and G2-geometries of contact Calabi-Yau 7-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-Nördstrom invariant of the natural G2-structure of the 7-dimens...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Physics Letters B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269324000753 |
| _version_ | 1797263002657882112 |
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| author | Daattavya Aggarwal Yang-Hui He Elli Heyes Edward Hirst Henrique N. Sá Earp Tomás S.R. Silva |
| author_facet | Daattavya Aggarwal Yang-Hui He Elli Heyes Edward Hirst Henrique N. Sá Earp Tomás S.R. Silva |
| author_sort | Daattavya Aggarwal |
| collection | DOAJ |
| description | We propose a machine learning approach to study topological quantities related to the Sasakian and G2-geometries of contact Calabi-Yau 7-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-Nördstrom invariant of the natural G2-structure of the 7-dimensional link of a weighted projective Calabi-Yau 3-fold hypersurface singularity, for 7549 of the 7555 possible P4(w) projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the P4(w) weights alone, using both neural networks and a symbolic regressor which achieve R2 scores of 0.969 and 0.993 respectively. Additionally, properties of the respective Gröbner bases are well-learnt, leading to a vast improvement in computation speeds which may be of independent interest. The data generation and analysis further induced novel conjectures to be raised. |
| first_indexed | 2024-03-07T23:24:58Z |
| format | Article |
| id | doaj.art-a1a8087917de424e99e34b11cbfb3591 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-04-25T00:06:05Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-a1a8087917de424e99e34b11cbfb35912024-03-14T06:13:17ZengElsevierPhysics Letters B0370-26932024-03-01850138517Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifoldsDaattavya Aggarwal0Yang-Hui He1Elli Heyes2Edward Hirst3Henrique N. Sá Earp4Tomás S.R. Silva5Department of Computer Science and Technology, University of Cambridge, CB3 0FD, UKDepartment of Mathematics, City, University of London, EC1V 0HB, UK; London Institute for Mathematical Sciences, Royal Institution, London, W1S 4BS, UK; Merton College, University of Oxford, OX1 4JD, UK; School of Physics, NanKai University, Tianjin, 300071, P.R. ChinaDepartment of Mathematics, City, University of London, EC1V 0HB, UK; London Institute for Mathematical Sciences, Royal Institution, London, W1S 4BS, UKCentre for Theoretical Physics, Queen Mary, University of London, E1 4NS, UK; Corresponding author.Institute of Mathematics, Statistics and Scientific Computing, University of Campinas (Unicamp), 13083-859, BrazilInstitute of Mathematics, Statistics and Scientific Computing, University of Campinas (Unicamp), 13083-859, BrazilWe propose a machine learning approach to study topological quantities related to the Sasakian and G2-geometries of contact Calabi-Yau 7-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-Nördstrom invariant of the natural G2-structure of the 7-dimensional link of a weighted projective Calabi-Yau 3-fold hypersurface singularity, for 7549 of the 7555 possible P4(w) projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the P4(w) weights alone, using both neural networks and a symbolic regressor which achieve R2 scores of 0.969 and 0.993 respectively. Additionally, properties of the respective Gröbner bases are well-learnt, leading to a vast improvement in computation speeds which may be of independent interest. The data generation and analysis further induced novel conjectures to be raised.http://www.sciencedirect.com/science/article/pii/S0370269324000753G2-manifoldsMachine learningHodge numbersCrowley-Nördstrom invariantContact Calabi-Yau manifolds |
| spellingShingle | Daattavya Aggarwal Yang-Hui He Elli Heyes Edward Hirst Henrique N. Sá Earp Tomás S.R. Silva Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds Physics Letters B G2-manifolds Machine learning Hodge numbers Crowley-Nördstrom invariant Contact Calabi-Yau manifolds |
| title | Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds |
| title_full | Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds |
| title_fullStr | Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds |
| title_full_unstemmed | Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds |
| title_short | Machine learning Sasakian and G2 topology on contact Calabi-Yau 7-manifolds |
| title_sort | machine learning sasakian and g2 topology on contact calabi yau 7 manifolds |
| topic | G2-manifolds Machine learning Hodge numbers Crowley-Nördstrom invariant Contact Calabi-Yau manifolds |
| url | http://www.sciencedirect.com/science/article/pii/S0370269324000753 |
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