Machine learning Calabi-Yau metrics

Abstract

We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kähler manifolds, we combine conventional curve fitting and machine-learning techniques to numerically approximate Ricci-flat metrics. We show that machine learning is able to predict the Calabi-Yau metric and quantities associated with it, such as its determinant, having seen only a small sample of training data. Using this in conjunction with a straightforward curve fitting routine, we demonstrate that it is possible to find highly accurate numerical metrics much more quickly than by using Donaldson's algorithm alone, with our new machine-learning algorithm decreasing the time required by between one and two orders of magnitude.

56 pages, 14 figures, references added

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• Machine Learning Lie Structures & Applications to Physics
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• Calabi-Yau Metrics, Energy Functionals and Machine-Learning
• Calabi-Yau CFTs and Random Matrices
• A Triumvirate of AI Driven Theoretical Discovery
• Brain Webs for Brane Webs
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• Machine learning complete intersection Calabi-Yau 3-folds
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• Row and column detection complexities of character tables
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