Machine learning Sasakian and G<inf>2</inf> topology on contact Calabi-Yau 7-manifolds

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 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.