Variational Evolutionary Network for Statistical Physics Systems

TL;DR

This paper introduces a variational evolutionary network that combines neural networks and evolutionary algorithms to improve importance sampling efficiency and accuracy in complex physical systems like spin glasses.

Contribution

It proposes a novel variational evolutionary network that enhances importance sampling by integrating neural networks with evolutionary algorithms for physical system simulations.

Findings

Provides an upper bound on ground-state energy.

Improves sampling efficiency and accuracy.

Demonstrates effectiveness on Ising and Sherrington-Kirkpatrick models.

Abstract

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and complex system simulations. However, these neural network-enhanced Monte Carlo methods still face challenges such as slow sampling speeds, statistical bias, and inaccuracies in the ground state. To address these issues, we propose a variational evolutionary network, which utilizes neural networks for variational free energy and combines evolutionary algorithms for sampling. During the sampling process, we construct generation and selection operators to filter samples based on importance, thereby achieving efficient importance sampling. We demonstrate that this sampling method provides an upper bound on the ground-state energy, enhancing both sampling efficiency and ground-state accuracy. Moreover, we numerically examine our method in two-dimensional Ising model and Sherrington-Kirkpatrick Model for spin glass. Thus, our algorithm could offer improved accuracy in handling complex energy landscapes and significantly enhance computational efficiency.