# Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality

arXiv: https://arxiv.org/abs/2309.05702 · HTML: https://mlsanity.com/paper/2309.05702/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 67 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 1 of 1)

- [Neurons on Amoebae](https://mlsanity.com/paper/2106.03695/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning BPS Spectra and the Gap Conjecture](https://mlsanity.com/paper/2405.09993/) (2024)
- [Machine Learning Toric Duality in Brane Tilings](https://mlsanity.com/paper/2409.15251/) (2024)
- [Generative AI for Brane Configurations and Coamoeba](https://mlsanity.com/paper/2411.16033/) (2024)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [Hamiltonian Neural Networks approach to fuzzball geodesics](https://mlsanity.com/paper/2502.20881/) (2025)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)
- [DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory](https://mlsanity.com/paper/2607.23614/) (2026)

## Abstract (arXiv)

We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a Type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associated to the toric Calabi-Yau 3-fold. When we vary the complex structure moduli of the mirror Calabi-Yau 3-fold, the coamoeba and the corresponding brane tilings change their shape, giving rise to different toric phases related by Seiberg duality. We illustrate that by employing techniques such as principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), we can project the space of coamoeba labelled by complex structure moduli down to a lower dimensional phase space with phase boundaries corresponding to Seiberg duality. In this work, we illustrate this technique by obtaining a 2-dimensional phase diagram for brane tilings corresponding to the cone over the zeroth Hirzebruch surface F0.