Neural and numerical methods for G2-structures on contact Calabi–Yau 7–manifolds

A numerical framework for approximating 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 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.