Calabi-Yau Metrics, Energy Functionals and Machine-Learning

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.