Optimal Low-dimensional Approximation of Transfer Operators via Flow Matching: Computation and Error Analysis
<|reference_start|>Optimal Low-dimensional Approximation of Transfer Operators via Flow Matching: Computation and Error Analysis: 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.<|reference_end|>
@article{zhang2024optimal,
    title={Optimal Low-dimensional Approximation of Transfer Operators via Flow
  Matching: Computation and Error Analysis},
    author={Zhicheng Zhang, Ling Guo, Hao Wu},
    journal={arXiv preprint arXiv:2408.15981},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15981},
    primaryClass={math.NA cs.NA math.DS}
}