# Generative AI for Brane Configurations and Coamoeba

arXiv: https://arxiv.org/abs/2411.16033 · HTML: https://mlsanity.com/paper/2411.16033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 94 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Machine Learning CICY Threefolds](https://mlsanity.com/paper/1806.03121/) (2018)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Machine Learning Calabi-Yau Four-folds](https://mlsanity.com/paper/2009.02544/) (2020)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Machine Learned Calabi-Yau Metrics and Curvature](https://mlsanity.com/paper/2211.09801/) (2022)
- [Searching the Landscape of Flux Vacua with Genetic Algorithms](https://mlsanity.com/paper/1907.10072/) (2019)
- [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)
- [Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality](https://mlsanity.com/paper/2309.05702/) (2023)
- [GANs for generating EFT models](https://mlsanity.com/paper/1809.02612/) (2018)
- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [Learning BPS Spectra and the Gap Conjecture](https://mlsanity.com/paper/2405.09993/) (2024)

## Built on by (most cited first, 2 of 2)

- [Hamiltonian Neural Networks approach to fuzzball geodesics](https://mlsanity.com/paper/2502.20881/) (2025)
- [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 a generative AI model to obtain Type IIB brane configurations that realize toric phases of a family of 4d N=1 supersymmetric gauge theories. These 4d N=1 quiver gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold. The Type IIB brane configurations are given by the coamoeba projection of the mirror curve associated with the toric Calabi-Yau 3-fold. The shape of the mirror curve and its coamoeba projection, as well as the corresponding Type IIB brane configuration and the toric phase of the 4d N=1 theory, all depend on the complex structure moduli parameterizing the mirror curve. We train a generative AI model, a conditional variational autoencoder (CVAE), that takes a choice of complex structure moduli as input and generates the corresponding coamoeba. This enables us not only to obtain a high-resolution representation of the entire phase space for a family of 4d N=1 theories corresponding to the same toric Calabi-Yau 3-fold, but also to continuously track the movements of the mirror curve and the branes wrapping the curve in the corresponding Type IIB brane configurations during phase transitions associated with Seiberg duality.