5 papers
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…
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…
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…
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…
Inferring Long-term Dynamics of Ecological Communities Using Combinatorics
William S. Cuello, Marcio Gameiro, Juan A. Bonachela +1
In an increasingly changing world, predicting the fate of species across the globe has become a major concern. Understanding how the population dynamics of various species and comm…