University of Cambridge > Talks.cam > Machine learning in Physics, Chemistry and Materials discussion group (MLDG) > Neural Network Approximations for Calabi-Yau Metrics

Neural Network Approximations for Calabi-Yau Metrics

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String theory is the only known consistent theory of quantum gravity. The extra-dimensional part of space posited by string theory is often described by complex geometries called Calabi—Yau manifolds. In order for string theory to make predictions for masses of fundamental particles, such as electrons, we require knowledge of a special Riemannian metric over Calabi—Yau threefolds. Such metrics, known as Ricci flat metrics, are solutions to partial differential equations that are notoriously difficult to solve. In fact, no analytic solution is known for metrics of Calabi—Yau threefolds. We employ techniques from machine learning to deduce numerical flat metrics for certain phenomenologically important Calabi—Yau geometries, namely, the Fermat quintic, the Dwork quintic, and the Tian-Yau manifold. 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.

This talk is part of the Machine learning in Physics, Chemistry and Materials discussion group (MLDG) series.

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