Variational Autoregressive Networks with probability priors

TL;DR

This paper introduces a physics-informed prior framework for neural network-based Monte Carlo sampling, improving training efficiency and enabling larger system simulations in spin models.

Contribution

It proposes a novel method that incorporates physical priors into neural networks, reducing training difficulty and enhancing performance in simulating spin systems.

Findings

Physics-informed priors improve training efficiency.

The method enables larger system size simulations.

Performance gains demonstrated on Ising and spin glass models.

Abstract

Monte Carlo methods are essential across diverse scientific fields, yet their efficiency is frequently hampered by critical slowing down-a sharp increase in autocorrelation times near phase transitions. Although deep learning approaches, such as neural-network-based samplers, have been proposed to alleviate this issue, they face another serious problem: the difficulty of training the models. This difficulty partially stems from the overly general nature of original machine-learning architectures, which often ignore underlying physical symmetries and force networks to relearn them from scratch. In this paper, we demonstrate that incorporating physical priors into the model significantly enhances performance. Building upon existing strategies that integrate spin-spin interactions, we propose a framework that utilizes a prior probability distribution as a starting point for training. Our results for the Ising model, as well as for the Edwards-Anderson spin glass model, suggest that moving away from `blank slate' models in favor of physics-informed priors reduces the training burden and facilitates the simulation of larger system sizes in discrete spin models.