Lattice QFT with continuous normalizing flows

This repository contains an implementation of continuous normalizing flows for scalar quantum field theory using JAX and Haiku, as introduced in the paper Learning Lattice Quantum Field Theories with Equivariant Continuous Flows. Specifically, it focuses on ϕ⁴ theory as an example.

Installation and dependencies

The code can be installed as a package via pip install . from within the root directory of this project. However, to run the code with GPU support, JAX should be installed first following the instructions here.

To run the example scripts and the notebook below, the additional packages hydra and matplotlib are required (install for example with pip install hydra-core matplotlib).

Examples

Introduction

A step-by-step jupyter notebook with further explanations can be found in notebooks/train-and-mcmc.ipynb. It contains an example of training the normalizing flow and using it to generate samples with a Metropolis-Hastings MCMC step.

Loading network parameters

The notebooks/load-parameters.ipynb notebook demonstrates how to load previously trained parameters for the examples discussed in the paper.

Scripts

Two scripts for training networks as used in the paper are provided: example_single and example_conditional. These can be configured by modifying or adding to the configuration files in the folder configs/.

Note that training can be slow when running on the CPU. Especially for a smaller lattice the batch size can be reduced while still yielding good results: python example_single.py ++live_plotting=true ++batch_size=64.

Reference

If you find our work useful, please cite

@article{gerdes2022,
    author = "Gerdes, Mathis and de Haan, Pim and Rainone, Corrado and Bondesan, Roberto and Cheng, Miranda C. N.",
    title = "{Learning Lattice Quantum Field Theories with Equivariant Continuous Flows}",
    eprint = "2207.00283",
    archivePrefix = "arXiv",
    primaryClass = "hep-lat",
    month = "7",
    year = "2022"
}