提出新型采样方法BNEM，高效生成符合玻尔兹曼分布的独立样本。
BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching
- 基于噪声能量匹配构建扩散采样器，理论方差更低。
- 在40高斯混合与4粒子双阱模型上达到最优性能。
- 适合分子动力学等需高精度采样的科研场景。
在科学计算中，从玻尔兹曼分布高效生成独立同分布样本是一项关键挑战，例如在分子动力学中。本文旨在仅通过能量函数学习神经采样器，而非依赖玻尔兹曼分布的采样数据。我们提出一种基于扩散的能量匹配方法（Noised Energy Matching），理论上具有更低方差和更高复杂度。进一步引入一种新颖的自举技术，用于平衡偏差与方差。我们在二维40高斯混合模型（2D 40-GMM）和4粒子双阱势（DW-4）上评估了NEM与BNEM。实验结果表明，BNEM在保持更高鲁棒性的同时实现了当前最优性能。
原文摘要 · Abstract (English)
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.
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