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Calabi-Yau Metrics, Energy Functionals and Machine-Learning

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.