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arXiv · 2602.12438

Neural and numerical methods for $\mathrm{G}_2$-structures on contact Calabi-Yau 7-manifolds

Elli Heyes·Edward Hirst·Henrique N. Sá Earp·Tomás S. R. Silva
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Abstract

A numerical framework for approximating $\mathrm{G}_2$-structure 3-forms on contact Calabi-Yau manifolds is presented. The approach proceeds in three stages: first, existing neural network models are employed to compute an approximate Ricci-flat metric on a Calabi-Yau threefold. Second, using this metric and the explicit construction of a $\mathrm{G}_2$-structure on the associated 7-dimensional Calabi-Yau link in the 9-sphere, numerical approximations of the 3-form are generated on a large set of sampled points. Finally, a dedicated neural architecture is trained to learn the 3-form and its induced Riemannian metric directly from data, validating the learned structure and its torsion via a numerical implementation of the exterior derivative, which may be of independent interest.

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Elli Heyes, Edward Hirst, Henrique N. Sá Earp, Tomás S. R. Silva. 2026-02-12. Neural and numerical methods for $\mathrm{G}_2$-structures on contact Calabi-Yau 7-manifolds. https://arxiv.org/abs/2602.12438

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