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Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithm
Paper Details
Published: 2024/10/15
DOI: 10.48550/arXiv.2410.11284
ARXIV ID: 2410.11284v1
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PDFMotivated by recent progress in the problem of numerical Kähler metrics, the authors survey machine learning techniques in this area, discussing both advantages and drawbacks. The authors present a novel approach to obtaining Ricci-flat approximations to Kähler metrics, applying machine learning within a `principled’ framework. In particular, they use gradient descent on the Grassmannian manifold to identify an efficient subspace of sections for calculation of the metric. This approach is combined with both Donaldson’s algorithm and learning on the h-matrix itself. The methods are implemented on the Dwork family of threefolds, commenting on the behaviour at different points in moduli space.
