Machine learning Sasakian and G₂ topology on contact Calabi-Yau 7-manifolds

We propose a machine learning approach to study topological quantities related to the Sasakian and G(2)-geometries of contact Calabi-Yau 7-manifolds. Specifically, we compute datasets for certain Sasakian Hodge numbers and for the Crowley-N & ouml;rdstrom invariant of the natural G(2)-structure of the 7-dimensional link of a weighted projective Calabi-Yau 3-fold hypersurface singularity, for 7549 of the 7555 possible P-4(w) projective spaces. These topological quantities are then machine learnt with high performance scores, where learning the Sasakian Hodge numbers from the P-4(w) weights alone, using both neural networks and a symbolic regressor which achieve R-2 scores of 0.969 and 0.993 respectively. Additionally, properties of the respective Gr & ouml;bner 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.