Generative models for sampling of lattice field theories

TL;DR

This paper introduces a self-learning generative model-based Markov chain Monte Carlo method for lattice field theories, demonstrating improved system size exploration and efficiency without pre-training, with applications to scalar ^4 theory.

Contribution

It presents a novel self-learning MCMC approach using generative models that enhances sampling efficiency and scalability in lattice field theories without requiring pre-existing training data.

Findings

Increased system sizes explored with the method.

Faster inference compared to traditional methods.

Good ergodicity and mixing properties observed.

Abstract

We explore a self-learning Markov chain Monte Carlo method based on the Adversarial Non-linear Independent Components Estimation Monte Carlo, which utilizes generative models and artificial neural networks. We apply this method to the scalar $\varphi^4$ lattice field theory in the weak-coupling regime and, in doing so, greatly increase the system sizes explored to date with this self-learning technique. Our approach does not rely on a pre-existing training set of samples, as the agent systematically improves its performance by bootstrapping samples collected by the model itself. We evaluate the performance of the trained model by examining its mixing time and study the ergodicity of generated samples. When compared to methods such as Hamiltonian Monte Carlo, this approach provides unique advantages such as the speed of inference and a compressed representation of Monte Carlo proposals for potential use in downstream tasks.