能量加权流匹配：解锁连续归一化流以实现高效且可扩展的玻尔兹曼采样
Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling
AI总结：
本文提出能量加权流匹配方法，通过仅使用能量函数评估，使连续归一化流能够高效建模玻尔兹曼分布，在55粒子伦纳德-琼斯簇等挑战性系统中实现高质量采样，减少能量评估次数达三个数量级。
摘要：
从非标准化目标分布（如玻尔兹曼分布μ_target(x) ∝ exp(-E(x)/T)）采样对许多科学应用至关重要，但因复杂的高维能量景观而计算上具有挑战性。现有方法应用现代生成模型到玻尔兹曼分布时，要么需要大量从目标分布抽取的样本，要么在仅使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。为解决这些不足，我们引入能量加权流匹配（EWFM），一种新的训练目标，使连续归一化流能够仅使用能量函数评估来建模玻尔兹曼分布。我们的目标通过重要性采样重新公式化条件流匹配，允许使用任意提案分布的样本进行训练。基于此目标，我们开发了两种算法：迭代EWFM（iEWFM），通过迭代训练逐步优化提案；以及退火EWFM（aEWFM），在具有挑战性的能量景观中进一步引入温度退火。在基准系统中，包括具有挑战性的55粒子伦纳德-琼斯簇，我们的算法在样本质量上与已建立的能量-only方法相当，同时要求的能量评估次数减少多达三个数量级。
英文摘要：
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.
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