3 papers
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…
math.DS2024
Global Dynamics of Ordinary Differential Equations: Wall Labelings, Conley Complexes, and Ramp Systems
Marcio Gameiro, Tomáš Gedeon, Hiroshi Kokubu +5
We introduce a combinatorial topological framework for characterizing the global dynamics of ordinary differential equations (ODEs). The approach is motivated by the study of gene…