仅用能量函数评估即可训练连续归一化流,实现高效分子采样。
Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling
- 基于重要性采样重构条件流匹配,支持任意提议分布训练
- 在55粒子系统上样本质量媲美主流方法,能量评估次数减少1000倍
- 适合需要低计算成本采样的分子模拟与物理建模场景
从非归一化目标分布(如玻尔兹曼分布 $μ_{\text{target}}(x) \propto \exp(-E(x)/T)$)采样是诸多科学应用的基础,但因复杂高维能量景观而计算困难。现有方法要么依赖大量目标分布样本,要么仅用能量评估训练时无法有效利用先进架构(如连续归一化流)的表达能力。为此,我们提出能量加权流匹配(EWFM),仅需能量函数评估即可训练连续归一化流以建模玻尔兹曼分布。该方法通过重要性采样重构条件流匹配,支持任意提议分布训练。基于此,我们设计两种算法:迭代EWFM(iEWFM)通过迭代精炼提议分布,以及退火EWFM(aEWFM)额外引入温度退火以应对复杂能量景观。在基准系统(包括55粒子的Lennard-Jones簇)上,我们的方法样本质量与现有能量仅限方法相当,同时能量评估次数减少达三个数量级。
原文摘要 · Abstract (English)
Sampling from unnormalized target distributions, e.g.\ Boltzmann distributions $μ_{\text{target}}(x) \propto \exp(-E(x)/T)$, is fundamental to many scientific applications yet computationally challenging due to complex, high-dimensional energy landscapes. Existing approaches applying modern generative models to Boltzmann distributions either require large datasets of samples drawn from the target distribution or, when using only energy evaluations for training, cannot efficiently leverage the expressivity of advanced architectures like continuous normalizing flows that have shown promise for molecular sampling. To address these shortcomings, we introduce Energy-Weighted Flow Matching (EWFM), a novel training objective enabling continuous normalizing flows to model Boltzmann distributions using only energy function evaluations. Our objective reformulates conditional flow matching via importance sampling, allowing training with samples from arbitrary proposal distributions. Based on this objective, we develop two algorithms: iterative EWFM (iEWFM), which progressively refines proposals through iterative training, and annealed EWFM (aEWFM), which additionally incorporates temperature annealing for challenging energy landscapes. On benchmark systems, including challenging 55-particle Lennard-Jones clusters, our algorithms demonstrate sample quality competitive with established energy-only methods while requiring up to three orders of magnitude fewer energy evaluations.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。