BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching

TL;DR

This paper introduces BNEM, a neural sampler based on bootstrapped noised energy matching, which efficiently generates independent samples from Boltzmann distributions with improved variance and robustness.

Contribution

The paper proposes a novel diffusion-based neural sampler with a bootstrapping technique, achieving lower variance and better performance than existing methods.

Findings

BNEM achieves state-of-the-art performance on GMM and DW-4 tasks.

BNEM demonstrates increased robustness compared to related methods.

Theoretical analysis shows lower variance of the proposed sampler.

Abstract

Developing an efficient sampler capable of generating independent and identically distributed (IID) samples from a Boltzmann distribution is a crucial challenge in scientific research, e.g. molecular dynamics. In this work, we intend to learn neural samplers given energy functions instead of data sampled from the Boltzmann distribution. By learning the energies of the noised data, we propose a diffusion-based sampler, Noised Energy Matching, which theoretically has lower variance and more complexity compared to related works. Furthermore, a novel bootstrapping technique is applied to NEM to balance between bias and variance. We evaluate NEM and BNEM on a 2-dimensional 40 Gaussian Mixture Model (GMM) and a 4-particle double-well potential (DW-4). The experimental results demonstrate that BNEM can achieve state-of-the-art performance while being more robust.