Asymptotically unbiased estimation of physical observables with neural samplers

TL;DR

This paper introduces a framework for unbiased estimation of physical observables using neural samplers, enabling accurate calculations of quantities like free energy and entropy in physical systems.

Contribution

It presents asymptotically unbiased estimators for observables with neural samplers, including those dependent on the partition function, and demonstrates their effectiveness in physical models.

Findings

Outperforms existing methods in 2D Ising model simulations

Provides variance estimators for observables

Enhances applicability of neural samplers to real-world physics

Abstract

We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the 2d Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.