Numerical metrics for complete intersection and Kreuzer–Skarke Calabi–Yau manifolds

Abstract We introduce neural networks (NNs) to compute numerical Ricci-flat Calabi–Yau (CY) metrics for complete intersection and Kreuzer–Skarke (KS) CY manifolds at any point in Kähler complex structure moduli space, the package cymetric which provides computation realizations of these techniques. In particular, we develop computationally realize methods point-sampling on manifolds. The training NNs is carried out subject a custom loss function. class fixed by adding component enforces slopes certain line bundles match with topological computations. Our are applied various manifolds, including quintic manifold, bi-cubic manifold KS Picard number two. show that volumes bundle can be reliably computed from resulting metrics. also apply our results an approximate Hermitian–Yang–Mills connection specific bi-cubic.