# Neural and numerical methods for G2-structures on contact Calabi-Yau 7-manifolds

arXiv: https://arxiv.org/abs/2602.12438 · HTML: https://mlsanity.com/paper/2602.12438/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [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)
- [Metric Flows with Neural Networks](https://mlsanity.com/paper/2310.19870/) (2023)

## Built on by (most cited first, 4 of 4)

- [Minimising Willmore Energy via Neural Flow](https://mlsanity.com/paper/2604.04321/) (2026)
- [PINNs in More General Geometry](https://mlsanity.com/paper/2604.25020/) (2026)
- [Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information](https://mlsanity.com/paper/2607.05492/) (2026)
- [A penalised Saito functional for heuristic search of free line arrangements](https://mlsanity.com/paper/2604.02995/) (2026)

## Abstract (arXiv)

A numerical framework for approximating G2-structure 3-forms on contact Calabi-Yau manifolds is presented. The approach proceeds in three stages: first, existing neural network models are employed to compute an approximate Ricci-flat metric on a Calabi-Yau threefold. Second, using this metric and the explicit construction of a G2-structure on the associated 7-dimensional Calabi-Yau link in the 9-sphere, numerical approximations of the 3-form are generated on a large set of sampled points. Finally, a dedicated neural architecture is trained to learn the 3-form and its induced Riemannian metric directly from data, validating the learned structure and its torsion via a numerical implementation of the exterior derivative, which may be of independent interest.