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arXiv · 2505.17302

Rigorously Characterizing Dynamics with Machine Learning

Marcio Gameiro·Brittany Gelb·Konstantin Mischaikow
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Abstract

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.

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Marcio Gameiro, Brittany Gelb, Konstantin Mischaikow. 2025-05-22. Rigorously Characterizing Dynamics with Machine Learning. https://arxiv.org/abs/2505.17302

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