Machine Learning Line Bundle Cohomology

Understand

We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds.

• Standard function learning based on simple fully connected networks with logistic sigmoids is reviewed and its main features and shortcomings are discussed.
• It has been observed recently that line bundle cohomology can be described by dividing the Picard lattice into certain regions in each of which the cohomology dimension is described by a polynomial formula.
• Based on this structure, we set up a network capable of identifying the regions and their associated polynomials, thereby effectively generating a conjecture for the correct cohomology formula.