Dynamical System Analysis for Data Science

Catalog description

The purpose of this course is to study the modern perspective on Data-driven Dynamical Systems. Specifically, we will focus on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. Dynamic mode decomposition, Koopman operators, diffusion maps, equations free modeling, Lagrangian coherent systems, finite-time Lyapunov exponents — are some of the new methods that have been introduced in recent decades to analyze dynamical systems. The lectures will survey these methods along with earlier ones of “nonlinear time series analysis.” The goal will be to describe theoretical principles and algorithmic approaches suitable for working with empirical data and computer defined systems.