# Approximate Ricci-flat Metrics for Calabi-Yau Manifolds

arXiv: https://arxiv.org/abs/2506.15766 · HTML: https://mlsanity.com/paper/2506.15766/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 18 Jun 2025.

## Builds on (most cited first, 5 of 5)

- [Neural Network Approximations for Calabi-Yau Metrics](https://mlsanity.com/paper/2012.15821/) (2020)
- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Machine learning Calabi-Yau metrics](https://mlsanity.com/paper/1910.08605/) (2019)
- [Calabi-Yau Metrics, Energy Functionals and Machine-Learning](https://mlsanity.com/paper/2112.10872/) (2021)
- [Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2412.19778/) (2024)

## Built on by (most cited first, 1 of 1)

- [Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation](https://mlsanity.com/paper/2602.07834/) (2026)

## Abstract (arXiv)

We outline a method to determine analytic K"ahler potentials with associated approximately Ricci-flat K"ahler metrics on Calabi-Yau manifolds. Key ingredients are numerically calculating Ricci-flat K"ahler potentials via machine learning techniques and fitting the numerical results to Donaldson's Ansatz. We apply this method to the Dwork family of quintic hypersurfaces in mathbbP4 and an analogous one-parameter family of bi-cubic CY hypersurfaces in mathbbP2×mathbbP2. In each case, a relatively simple analytic expression is obtained for the approximately Ricci-flat K"ahler potentials, including the explicit dependence on the complex structure parameter. We find that these K"ahler potentials only depend on the modulus of the complex structure parameter.