Neural Network Approximations for Calabi-Yau Metrics

• URL: http://arxiv.org/abs/2012.15821v2
• Date: Wed, 27 Jan 2021 18:57:02 GMT
• Title: Neural Network Approximations for Calabi-Yau Metrics
• Authors: Vishnu Jejjala, Damian Kaloni Mayorga Pena, Challenger Mishra
• Abstract summary: We employ techniques from machine learning to deduce numerical flat metrics for the Fermat quintic, for the Dwork quintic, and for the Tian-Yau manifold. We show that measures that assess the Ricci flatness of the geometry decrease after training by three orders of magnitude.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 the Fermat quintic, for the Dwork quintic, and for the Tian-Yau manifold. This investigation employs a single neural network architecture that is capable of approximating Ricci flat Kaehler metrics for several Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness of the geometry decrease after training by three orders of magnitude. This is corroborated on the validation set, where the improvement is more modest. Finally, we demonstrate that discrete symmetries of manifolds can be learned in the process of learning the metric.

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