Calabi–Yau metrics, energy functionals and machine learning

Abstract

In this paper, 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 Kähler potential of a Calabi–Yau metric having seen only a small sample of training data.