Neural Network Approximations for Calabi-Yau Metrics

  title={Neural Network Approximations for Calabi-Yau Metrics},
  author={Vishnu Jejjala and Dami{\'a}n Kaloni Mayorga Pe{\~n}a and Challenger Mishra},
Abstract Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for K3, the Fermat quintic, and the Dwork quintic. This investigation employs a simple, modular neural network architecture that is capable of approximating Ricci flat Kähler metrics for Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness and consistency of the metric… 

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