Learning Size and Shape of Calabi-Yau Spaces

Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle, Robin Schneider

Preprint number: UUITP-53/21

Abstract: We present a new machine learning library for computing metrics of string compactification spaces. We benchmark the performance on Monte-Carlo sampled integrals against previous numerical approximations and find that our neural networks are more sample- and computation-efficient. We are the first to provide the possibility to compute these metrics for arbitrary, user-specified shape and size parameters of the compact space and observe a linear relation between optimization of the partial differential equation we are training against and vanishing Ricci curvature.