Applied Mathematics Seminar | Navaratnam Sri Namachchivaya, Random and Data Driven Dynamical Systems

Thursday, March 2, 2017 2:30 pm - 2:30 pm EST (GMT -05:00)

MC 5417

Speaker

Professor Navaratnam Sri Namachchivaya
Director, Nonlinear Systems Group | Department of Aerospace Engineering
University of Illinois @ Urbana-Champaign

Title

Random and Data Driven Dynamical Systems

Abstract

I will present a general overview of several engineered and natural systems with uncertain mathematical models, the multidisciplinary methods required for their analysis, and relevant results. The collection of new mathematical techniques that I will describe lies at the confluence of three important areas: dynamical systems; control and estimation (data assimilation); and information theory. The first part of the talk focuses on the challenges in data assimilation that arise from the interactions between uncertainties, nonlinearities, and observations. I will present rigorous reduced-order data assimilation techniques for high dimensional multi-scale problems. In particular, I will outline how scaling interacts with filtering via stochastic averaging. Optimal sensor placement based on information theoretic concepts will also be discussed. The second part of the talk brings together three interesting themes in dynamical systems — resonances, domains of attraction, and large deviations. The subtleties of their interactions are explored in a canonical way by combining the ideas from dynamical systems, homogenization methods, and large deviations.