Machine learning Calabi-Yau metrics. (English) Zbl 1537.53003
Summary: 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.
© 2020 Wiley-VCH GmbH
© 2020 Wiley-VCH GmbH
MSC:
| 53-08 | Computational methods for problems pertaining to differential geometry |
| 53D18 | Generalized geometries (à la Hitchin) |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 32Q25 | Calabi-Yau theory (complex-analytic aspects) |
| 68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 68T07 | Artificial neural networks and deep learning |
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