AI 中文总结
本文针对采样与优化中核心的Gibbs概率测度计算问题，引入带增强耗散的输运-扩散动力学，设计了对应的采样数值算法与粒子系统。
AI 中文摘要
众所周知，Gibbs概率测度 $e^{-\mathbb{U}(\mathbf{x})}/Z$ 的计算实现，在采样与优化中发挥着核心作用。本文引入两类动力学，其能快速收敛至这些Gibbs测度，快速收敛的机制是这类输运-扩散动力学伴随的增强耗散。受此增强动力学启发，我们设计了从目标Gibbs测度采样的数值算法，最后给出了相应的粒子系统，该系统可衍生出其他有效的数值采样器。
英文摘要
It is well known that the computational realization of Gibbs probability measures, $e^{-\mathbb{U}(\mathbf{x})}/Z$, plays a central role in sampling and optimization. In this paper, we introduce two types of dynamics that exhibit rapid convergence towards these Gibbs measures. The mechanism driving this rapid convergence is the enhanced dissipation associated with these transport-diffusion dynamics. Motivated by these enhanced dynamics, we design numerical algorithms for sampling from the target Gibbs measure. Finally, we provide the corresponding particle systems that may yield other effective numerical samplers.
