Calabi-Yau Metrics, Energy Functionals and Machine-Learning

TL;DR

This paper demonstrates that machine learning can accurately predict Calabi-Yau metrics, including the optimal Ricci-flat metrics, using limited training data, advancing numerical methods in complex geometry.

Contribution

It extends previous machine learning approaches to more accurate Calabi-Yau metrics, surpassing earlier approximations with fewer training samples.

Findings

Machine learning predicts Kähler potentials effectively.

ML models improve accuracy of Ricci-flat metric approximations.

Limited training data suffices for high-quality predictions.

Abstract

We apply machine learning to the problem of finding numerical Calabi-Yau metrics. We extend previous work on learning approximate Ricci-flat metrics calculated using Donaldson's algorithm to the much more accurate "optimal" metrics of Headrick and Nassar. We show that machine learning is able to predict the K\"ahler potential of a Calabi-Yau metric having seen only a small sample of training data.