Papers › Machine learning Sasakian and G₂ topology on contact Calabi-Yau 7-manifolds
Machine learning Sasakian and G₂ topology on contact Calabi-Yau 7-manifolds
Daattavya Aggarwal, Yang-Hui He, Elli Heyes, Edward Hirst, Henrique N. Sá Earp, Tomás S. R. Silva
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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-N\"ordstrom 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 Gr\"obner 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.
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