Abstract

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 each of the 7555 possible ℙ4(w) projective spaces. These topological quantities are then machine learnt with high accuracy, along with properties of the respective Gröbner basis, leading to a vast improvement in computation speeds which may be of independent interest. We observe promising results in machine 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, inducing novel conjectures to be raised.

https://arxiv.org/abs/2310.03064