Learning Size and Shape of Calabi-Yau Spaces

TL;DR

This paper introduces a machine learning library that efficiently computes metrics of Calabi-Yau spaces, enabling flexible shape and size analysis with improved accuracy and efficiency over previous methods.

Contribution

It presents the first neural network-based approach capable of computing metrics for arbitrary parameters of Calabi-Yau spaces, demonstrating a linear relation with Ricci curvature optimization.

Findings

Neural networks outperform previous numerical methods in sample and computation efficiency.

The library allows for arbitrary shape and size parameter inputs.

A linear relation between PDE optimization and Ricci curvature is observed.

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.