Machine Learning Calabi-Yau Metrics

Anthony Ashmore

doi:10.1002/prop.202000068

Machine Learning Calabi-Yau Metrics

2020-08-12

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DOI：10.1002/prop.202000068

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We apply machine learning to the problem of finding numerical Calabi-Yau metrics. Building on Donaldson's algorithm for calculating balanced metrics on Kahler 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.

Keyword:

generalized geometry

supergravity backgrounds

Machine Learning Calabi-Yau Metrics

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