The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not computable. We recall a coarser characterization of dynamics based on order theory and algebraic topology and prove that this characterization can be identified using approximations.
@article{arxiv.2505.17302,
title = {Rigorously Characterizing Dynamics with Machine Learning},
author = {Marcio Gameiro and Brittany Gelb and Konstantin Mischaikow},
journal= {arXiv preprint arXiv:2505.17302},
year = {2025}
}