迭代去噪能量匹配用于从玻尔兹曼密度中采样
Iterated Denoising Energy Matching for Sampling from Boltzmann Densities
AI总结：
提出迭代去噪能量匹配（iDEM），利用能量函数及其梯度训练扩散采样器，无需数据样本，实现高效采样，性能最优且训练快2-5倍，首次用于55粒子Lennard-Jones系统。
摘要：
从未归一化的概率分布中高效生成统计上独立的样本，例如多体系统的平衡样本，是科学中的一个基础问题。在本文中，我们提出了迭代去噪能量匹配（iDEM），一种迭代算法，该算法利用一种新颖的随机分数匹配目标，仅依靠能量函数及其梯度——无需数据样本——来训练基于扩散的采样器。具体来说，iDEM交替进行（I）从基于扩散的采样器中采样高模型密度区域，以及（II）使用这些样本在我们的随机匹配目标中进一步改进采样器。iDEM可扩展到高维，因为内部匹配目标是免模拟的，并且不需要MCMC样本。此外，通过利用扩散的快速模式混合行为，iDEM平滑了能量景观，从而实现高效的探索和学习摊销采样器。我们在从标准合成能量函数到不变的$n$体粒子系统的一系列任务上评估iDEM。我们表明，所提出的方法在所有指标上达到了最先进的性能，并且训练速度快$2-5$倍，这使其成为第一个使用能量在具有挑战性的$55$粒子Lennard-Jones系统上训练的方法。
英文摘要：
Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
