标题： 基于机器学习的条件路径测度采样 显示英文标题

标题： Machine-Learned Sampling of Conditioned Path Measures

摘要： 我们提出了从一般先验过程下的后验路径测度$P(C([0, T], \mathbb{R}^d))$抽样的算法。 这利用了以下思想：(1) 受控平衡动力学，它可以在两个路径测度之间逐渐传输；(2) 在具有Wasserstein度量的$\infty$维概率空间中的优化，可用于在指定似然函数下演化密度曲线。 由此产生的算法有坚实的理论基础，并且可以无缝地与神经网络集成，以学习目标轨迹集合，而无需访问数据。 显示英文摘要

摘要： We propose algorithms for sampling from posterior path measures $P(C([0, T], \mathbb{R}^d))$ under a general prior process. This leverages ideas from (1) controlled equilibrium dynamics, which gradually transport between two path measures, and (2) optimization in $\infty$-dimensional probability space endowed with a Wasserstein metric, which can be used to evolve a density curve under the specified likelihood. The resulting algorithms are theoretically grounded and can be integrated seamlessly with neural networks for learning the target trajectory ensembles, without access to data.