  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. For complex surfaces, we also set up a network
which learns certain rigid divisors which appear in a recently discovered
master formula for cohomology dimensions.
