Exploring Group Convolutional Networks for Sign Problem Mitigation via Contour Deformation

TL;DR

This paper investigates the use of group convolutional neural networks to improve the mitigation of the sign problem in quantum Monte Carlo simulations, focusing on accuracy, training efficiency, and transfer learning capabilities.

Contribution

It introduces the application of group convolutional models to the sign problem, comparing their performance to fully connected networks and exploring transfer learning benefits.

Findings

Group convolutional networks outperform fully connected networks in sign problem mitigation.

Encoding physical symmetries into neural networks enhances accuracy and training speed.

Transfer learning reduces training costs in sign problem simulations.

Abstract

The sign problem that arises in Hybrid Monte Carlo calculations can be mitigated by deforming the integration manifold. While simple transformations are highly efficient for simulation, their efficacy systematically decreases with decreasing temperature and increasing interaction. Machine learning models have demonstrated the ability to push further, but require additional computational effort and upfront training. While neural networks possess the capacity to learn physical symmetries through proper training, there are anticipated advantages associated with encoding them into the network's structure. These include enhanced accuracy, accelerated training, and improved stability. The objective of the present study is twofold. First, we investigate the benefits of group convolutional models in comparison to fully connected networks, with a specific focus on the effects on the sign problem and on computational aspects. Second, we examine their capabilities for transfer learning, demonstrating the ability to further reduce training cost. We perform our investigations on the Hubbard model on select low-dimensional systems.