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We introduce neural networks to compute numerical Ricci-flat CY metrics forcomplete intersection and Kreuzer-Skarke Calabi-Yau manifolds at any point inK\"ahler and complex structure moduli space, and introduce the package cymetricwhich provides computation realizations of these techniques. In particular, wedevelop and computationally realize methods for point-sampling on thesemanifolds. The training for the neural networks is carried out subject to acustom loss function. The K\"ahler class is fixed by adding to the loss acomponent which enforces the slopes of certain line bundles to match withtopological computations. Our methods are applied to various manifolds,including the quintic manifold, the bi-cubic manifold and a Kreuzer-Skarkemanifold with Picard number two. We show that volumes and line bundle slopescan be reliably computed from the resulting Ricci-flat metrics. We also applyour results to compute an approximate Hermitian-Yang-Mills connection on aspecific line bundle on the bi-cubic.

Numerical Metrics for Complete Intersection and Kreuzer-Skarke Calabi-Yau Manifolds