2024/08/28 by Zhicheng Zhang, Ling Guo, Zhang, Zhicheng +3
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2408.15981
openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.