Learning Size and Shape of Calabi-Yau Spaces
arXiv:2111.01436
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.
arXiv comment5 pages, 2 figures, to appear in: NeurIPS 2021 - ML4PS
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