用机器学习方法高效采样条件路径分布，无需真实数据。
Machine-Learned Sampling of Conditioned Path Measures
- 结合平衡动力学与无限维优化，构建路径采样新算法。
- 可直接与神经网络集成，学习目标轨迹集合。
- 适用于无数据场景的轨迹生成与模拟任务。
我们提出针对一般先验过程下后验路径测度 $P(C([0, T], bR^d))$ 的采样算法。该方法融合了（1）受控平衡动力学，实现两路径测度间的渐进传输；以及（2）在配备 Wasserstein 度量的无穷维概率空间中的优化，可沿指定似然演化密度曲线。所提算法具有理论基础，能无缝集成神经网络以学习目标轨迹集合，且无需访问真实数据。
原文摘要 · Abstract (English)
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.
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