Treffer: Nonlinear dynamics and data driven modeling

The research areas of dynamics and data-driven modeling overlap in existing literature. Some research uses dynamical systems as a test bed while developing new modeling methods. Other papers attempt to use data-driven modeling as a tool to better understand, or potentially predict the behavior of a dynamical system. The primary goal of this thesis is to further the symbiotic relationship between these two research areas. Firstly, this paper provides a concrete example of how a basis function decomposition of the Lorenz system can provide a quantitative performance metric for data-driven modeling methods. Secondly, a novel application of an existing modeling method will yield an unexpected Lorenz-Like equation. Finally, this paper discusses preliminary work toward a novel application of data-driven modeling in the field of optics, a research area that remains at the edge of human knowledge. By exploring these three topics, which exist in the intersection of dynamics and data- driven modeling, this thesis aims to provide tools, insights, and intuition that will aid collaborative research of dynamics and data-driven modeling.