thesfinox/ml-cicy-4folds

Machine Learning for Calabi-Yau 4-folds

AI for CICY 4-folds

H. Erbin (MIT), R. Finotello (CEA Paris-Saclay), R. Schneider (Uppsala U.), M. Tamaazousti (CEA Paris-Saclay)

Paper: arXiv:2108.02221 Code (in this repo): R. Finotello

See also R. Schneider's repo for additional material such as classification tasks and hyperparameter optimisation.

Abstract

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau (CY) manifolds using deep learning. In this paper, we consider the dataset of all CY four-folds constructed as complete intersections (CICY) in products of projective spaces. Employing neural networks inspired from state-of-the-art computer vision architectures, we introduce the model CICYMiner and we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task regression architecture.

Requirements

Requirements are specified in requirements.yml for a Conda environment using Python 3.6 and Tensorflow 2.1. Use the command conda env create -n cicy -f requirements.yml (see also here) to build an identical virtual environment on your local machine.

Usage Tips

The CICY dataset can be found here, and the original papers here and here.

Use sets.py to create training, validation and test sets according to your needs (use python sets.py - h for the list of options).

For hyperparameter optimisation with a grid search, use grid.py to form a JSON file with all possible hyperparameter options. Use python grid.py -h for the complete list of options. The list of choices should be specified in a JSON formatted file such as parameters.json and passed to grid.py (each parameter is a list of lists, in order to form the grid search)

Files cicy_*.py perform the training and inference tasks. Use python cicy.py -h for a list of options. Specifically, cicy.py performs the training on a single branch architecture, cicy_diff.py uses a multi-task architecture to compute all four Hodge numbers at once, cicy_diff_ablation.py performs an in-depth ablation study with respect to other architectures provided as hyperparameter choices.