Model
Digital Document
Publisher
Florida Atlantic University
Description
Dynamical systems play a pivotal role across various scientific domains, encompassing disciplines from physics to biology and engineering. The long-term behavior of these systems hinges on the structure of their attractors, with many exhibiting multistability characterized by multiple minimal attractors. Understanding the structure of these attractors and their corresponding basins is a central theme in dynamical systems theory.
In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.
In recent years, machine learning algorithms have emerged as potent tools for clustering, prediction, and modeling complex data. By harnessing the capabilities of neural networks along with techniques from topological data analysis, in particular persistence homology, we can construct surrogate models of system asymptotics. This approach also allows for the decomposition of phase space into polygonal regions and the identification of plausible attracting neighborhoods, facilitating homological Conley index computation at reduced computational expense compared to current methods. Through various illustrative examples, we demonstrate that sufficiently low training loss yields constructed neighborhoods whose homological Conley indices aligns with a priori knowledge of the dynamics.
Member of