Calabi-Yau Metrics, Energy Functionals and Machine-Learning
This work addresses a computational bottleneck in theoretical physics for researchers studying Calabi-Yau manifolds, representing an incremental improvement over prior methods.
The authors tackled the problem of finding numerical Calabi-Yau metrics by applying machine learning to predict Kähler potentials, achieving accurate predictions with only a small sample of training data.
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.