Numerical Calabi-Yau metrics from holomorphic networks

TL;DR

This paper introduces machine learning techniques to compute numerical Calabi-Yau metrics, demonstrating higher accuracy especially for manifolds lacking symmetry, and discusses optimization challenges.

Contribution

It presents novel machine learning methods for Calabi-Yau metric computation, outperforming previous approaches in accuracy for asymmetric manifolds.

Findings

Machine learning methods achieve higher accuracy.

Performance improves on manifolds with little symmetry.

Discusses overparameterization and optimization issues.

Abstract

We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat K\"ahler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods.