桥接随机流映射与玻尔兹曼生成器：基于归一化流的方法
Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
- Flatiron Institute（熨斗研究所）
- University of Cambridge（剑桥大学）
- Johns Hopkins University（约翰斯·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出NF$^2$M，结合随机流映射与归一化流构建玻尔兹曼生成器，通过逐步重加权去噪转换提升采样效率与样本质量，在肽系统上验证了有效性。
AI中文摘要：
在大规模生成分子系统的独立平衡样本仍然是计算统计力学中的核心障碍。玻尔兹曼生成器通过将生成模型与重要性采样配对，从目标分布中获得一致的样本来解决这一问题。我们引入了归一化流流映射（NF$^2$M），该方法结合了近期随机流映射的优势与经典归一化流的可处理性，构建了一个玻尔兹曼生成器。与大多数仅在最后修正生成模型的方法不同，NF$^2$M在生成过程中对每个去噪转换进行重新加权，避免了在最终被丢弃的轨迹上浪费计算资源。在每个去噪步骤中，条件归一化流根据当前噪声状态提出干净的构型（这比直接从目标分布采样更简单），其精确似然使得能够将每个提议修正为目标玻尔兹曼分布的真实去噪转换。这与大多数现有方法形成对比，这些方法的似然是近似或计算昂贵的，削弱了修正的统计可靠性。我们建立了修正转换的一致性，并界定了近似误差在采样链中的传播方式。我们在肽系统上评估了NF$^2$M，展示了改进的采样效率和样本质量。
英文摘要：
Generating independent, equilibrium samples of molecular systems at scale remains a central obstacle in computational statistical mechanics. Boltzmann Generators address this by pairing a generative model with importance sampling to obtain consistent samples from the target distribution. We introduce Normalizing Flow Flow Maps (NF$^2$M), which combines the strengths of recent stochastic flow maps with the tractability of classic normalizing flows to build a Boltzmann Generator. Unlike most methods, which correct the generative model only at the end, NF$^2$M reweighs each denoising transition as generation proceeds, avoiding wasted compute on trajectories that are ultimately discarded. At each denoising step, a conditional normalizing flow proposes clean configurations given the current noisy state (a simpler task than sampling directly from the target) and its exact likelihood enables correcting each proposal toward the true denoising transition of the target Boltzmann distribution. This is in contrast to most existing methods, whose likelihoods are approximate or expensive to evaluate, undermining the statistical reliability of the correction. We establish consistency of the corrected transitions and bound how approximation errors propagate through the sampling chain. We evaluate NF$^2$M on peptide systems, demonstrating improved sampling efficiency and sample quality.
