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Machine learning Calabi-Yau metrics

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arxiv 1910.08605 v2 pith:CUGDAGKB submitted 2019-10-18 hep-th math.AGstat.ML

Anthony Ashmore , Yang-Hui He , Burt Ovrut This is my paper
classification hep-thmath.AGstat.ML
keywords metricsalgorithmcalabi-yaulearningmachinecurvedonaldsonfitting
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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 K\"ahler 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.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  7. What to do with a Ricci-flat Calabi--Yau metric?

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.

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