提出一种可在无限维函数空间高效采样的新方法，用于模拟受罕见事件约束的扩散路径。
Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces
- 基于随机最大值原理，将最优控制思想拓展至函数空间采样
- 在合成势场与真实分子系统上均优于现有方法，如丙氨酸二肽和Chignolin
- 适合需要精确轨迹采样的复杂系统建模，如生物分子动力学
基于学习的有限维空间吉布斯分布采样方法进展迅速，但针对无限维函数空间的理论与算法仍不充分。这一差距制约了对条件扩散过程路径的采样能力，而后者在高效模拟满足罕见事件或边界约束的扩散轨迹方面具有巨大潜力。本文提出面向无限维函数空间的伴随采样器（Functional Adjoint Sampler, FAS），这是一种基于随机最优控制的扩散采样方法，直接在函数空间中操作，目标为无限维希尔伯特空间上的吉布斯型分布。FAS 基于随机最大值原理（stochastic maximum principle）将哈文斯等人（Havens et al., 2025）的伴随采样推广至希尔伯特空间，导出一种简洁可扩展的匹配型目标函数。实验表明，FAS 在合成势场及真实分子系统（包括丙氨酸二肽、Chignolin）中均展现出更优的过渡路径采样性能。
原文摘要 · Abstract (English)
Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional Adjoint Sampler (FAS) generalizes Adjoint Sampling (Havens et al., 2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.
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。