# Machine learning Calabi-Yau metrics

arXiv: https://arxiv.org/abs/1910.08605 · HTML: https://mlsanity.com/paper/1910.08605/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 23 of 23)

- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Machine Learned Calabi-Yau Metrics and Curvature](https://mlsanity.com/paper/2211.09801/) (2022)
- [Calabi-Yau Metrics, Energy Functionals and Machine-Learning](https://mlsanity.com/paper/2112.10872/) (2021)
- [Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds](https://mlsanity.com/paper/2112.09117/) (2021)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [A Machine Learning Approach to the Nirenberg Problem](https://mlsanity.com/paper/2602.12368/) (2026)
- [Constructing and Machine Learning Calabi-Yau Five-folds](https://mlsanity.com/paper/2310.15966/) (2023)
- [Calabi-Yau metrics through Grassmannian learning and Donaldson's algorithm](https://mlsanity.com/paper/2410.11284/) (2024)
- [Symbolic Approximations to Ricci-flat Metrics Via Extrinsic Symmetries of Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2412.19778/) (2024)
- [Neural and numerical methods for G2-structures on contact Calabi-Yau 7-manifolds](https://mlsanity.com/paper/2602.12438/) (2026)
- [cymyc -- Calabi-Yau Metrics, Yukawas, and Curvature](https://mlsanity.com/paper/2410.19728/) (2024)
- [Minimal surfaces, Knots, and Neural Networks](https://mlsanity.com/paper/2605.26234/) (2026)
- [Intelligent Explorations of the String Theory Landscape](https://mlsanity.com/paper/2204.08073/) (2022)
- [Machine-Learning Kronecker Coefficients](https://mlsanity.com/paper/2306.04734/) (2023)
- [Hamiltonian Neural Networks approach to fuzzball geodesics](https://mlsanity.com/paper/2502.20881/) (2025)
- [Approximate Ricci-flat Metrics for Calabi-Yau Manifolds](https://mlsanity.com/paper/2506.15766/) (2025)
- [Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation](https://mlsanity.com/paper/2602.07834/) (2026)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)
- [Learning to be Simple](https://mlsanity.com/paper/2312.05299/) (2023)
- [Machine Learning the 6d Supergravity Landscape](https://mlsanity.com/paper/2505.16131/) (2025)
- [Machine learning modularity](https://mlsanity.com/paper/2601.01779/) (2026)
- [GlobalCY I: A JAX Framework for Globally Defined and Symmetry-Aware Neural K"ahler Potentials](https://mlsanity.com/paper/2604.11404/) (2026)

## Abstract (arXiv)

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.