FUND：用于采样非归一化分布的密度流
FUND: Density Flow for Sampling Unnormalised Distributions
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中文总结 AI 辅助
提出FUND算法，通过分布轨迹匹配而非样本轨迹匹配，无需真实样本即可学习玻尔兹曼分布，在多个基准上超越MCMC和流基方法，实现高效采样与全面模式覆盖。
中文摘要 AI 辅助
从玻尔兹曼分布中进行高效采样对于模拟复杂物理系统至关重要。马尔可夫链蒙特卡洛（MCMC）方法存在临界慢化、高自相关性和较差的模式混合问题，限制了其可扩展性。最近的进展，如玻尔兹曼生成器，提供了一种有前景的替代方案，但仍受限于基于MCMC的昂贵训练、低效采样和较差的遍历性。我们提出了一种学习玻尔兹曼分布的算法，该算法在训练过程中不需要任何真实样本。我们的方法从流匹配中汲取灵感，但根本性地从样本轨迹匹配转向分布轨迹匹配。该算法迭代地重塑目标分布，利用模型生成的样本来指导学习并确保全面的模式覆盖。我们在标准基准上验证了我们的方法，包括二维高斯混合模型、多阱分布和高维标量φ^4理论。所提出的方法不仅相对于传统MCMC和基于流的基线提高了采样性能和准确性，还为无样本学习复杂物理分布建立了一种新方法。
英文摘要
Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $ϕ^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.
