Global invariant neural models for Kähler potentials outperform local baselines on geometric diagnostics for hard Calabi-Yau hypersurfaces.
Numerical Calabi-Yau metrics
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abstract
We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics, and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.
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2026 2roles
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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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GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural K\"ahler Potentials
Global invariant neural models for Kähler potentials outperform local baselines on geometric diagnostics for hard Calabi-Yau hypersurfaces.
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What to do with a Ricci-flat Calabi--Yau metric?
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.