Numerical Calabi-Yau metrics from holomorphic networks

Michael R Douglas

Abstract:

We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat
Kahler) metrics, and implement them using Tensorflow/Keras. We compare them with previous ¨
work, and find that they are far more accurate for manifolds with little or no symmetry. We also
discuss issues such as overparameterization and choice of optimization methods.