Reaction coordinates (RCs) are low-dimensional representations of complex dynamical systems that capture their long-term dynamics. In this work, we focus on the criteria of lumpability and decomposability, previously established for assessing RCs, and propose a new flow matching approach for the analysis and optimization of reaction coordinates based on these criteria. This method effectively utilizes data to quantitatively determine whether a given RC satisfies these criteria and enables end-to-end optimization of the reaction coordinate mapping model. Furthermore, we provide a theoretical analysis of the relationship between the loss function used in our approach and the operator error induced by dimension reduction.

翻译：反应坐标（RCs）是复杂动力学系统的低维表示，能够捕捉其长期动力学行为。本研究聚焦于先前建立的用于评估反应坐标的可聚合性与可分解性准则，并基于这些准则提出了一种新的流匹配方法，用于反应坐标的分析与优化。该方法能有效利用数据定量判定给定反应坐标是否满足这些准则，并实现反应坐标映射模型的端到端优化。此外，我们从理论上分析了本方法所用损失函数与降维引起的算子误差之间的关系。