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math.DS2026
Characterizing High-dimensional Dynamics by Combinatorial-Topological Methods on a Latent Space
Patrick Bailon, Marcio Gameiro, Brittany Gelb +5
Combinatorial-topological methods for characterizing dynamics are rigorous, generalizable, computable, and they only require approximations, but the dimension of the phase space is…
math.DS2025
Data-driven Identification of Attractors Using Machine Learning
Marcio Gameiro, Brittany Gelb, William Kalies +3
In this paper we explore challenges in developing a topological framework in which machine learning can be used to robustly characterize global dynamics. Specifically, we focus on…
math.DS2025
Rigorously Characterizing Dynamics with Machine Learning
Marcio Gameiro, Brittany Gelb, Konstantin Mischaikow
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 i…