Machine learning toric duality in brane tilings

This project aims to classify/identify Dimers which are equivalent under Seiberg duality.

We focus mostly on two cases:

• $\mathbb{Z}_m\times\mathbb{Z}_n$ orbifolds of the conifold
• the $Y^{6,0}$ dimer.

For the $\mathbb{Z}_m\times\mathbb{Z}_n$ orbifolds of the conifold, we train a fully connected network to predict the labels $(m,n)$. Whereas we trained a residual neural network to classify/predict the toric phases of the $Y^{6,0}$ dimer.

More information can be found in our original paper arxiv:2409.15251.

Python requirements

This project was created using specific python and tensorflow versions.

Important

• python version == 3.11.x (3.10.x on linux)
• tensorflow version == 2.16.1

The authors have not tested any other versions, and cannot guarantee a bug-free experience elsewise. All required packages can be found in the requirements.txt file.

Running our code

This repo contains code for training, evaluation and even dataset generation.

Evaluation

Both evaluation files for the fully connected and ResNet can be found in their respective sub-directories

DimerML
└───models
│   └───dense
│   |    └───evaluate.py
│   |    └───train.py
│   |    └───...
│   └───ResNet
│        └───evaluate.py
│        └───train.py
│        └───...
└───...

These contain a set of example Kasteleyn matrices and link to our model checkpoints. You can directly run them with the given parameters to get the model's outputs.

Training

If you wish to train your own network, with a different set of parameters, you must first unzip our datasets found in DimerML/datasets. You are then free to run the train.py files with your chosen parameters.

Dataset generation

Those who wish to generate a completely new dataset with either larger matrix sizes or more iterations can use the dataset_generator.py file. Note that this file requires one to unzip the ZmZn_matrices.zip.