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AM Seminar: Data-driven modeling and model reduction for chaotic dynamical systems

Speaker Name: 
Kevin Lin
Speaker Title: 
Associate Professor
Speaker Organization: 
University of Arizona Tucson
Start Time: 
Monday, May 13, 2019 - 4:00pm
End Time: 
Monday, May 13, 2019 - 5:00pm
BE 372
Daniele Venturi

Abstract Nonlinear dynamic phenomena often require a large number of dynamical variables for their description, only a small fraction of which are of direct interest.  Reduced models using only these relevant variables can be very useful in such situations, both for computational efficiency and insights into the underlying dynamics.  Unfortunately, except in special cases, deriving reduced models from first principles can be quite challenging.  This has led to interest in data-driven approaches to the construction of reduced models.  In this talk, I will review a discrete-time version of the Mori-Zwanzig (MZ) projection operator formalism from nonequilibrium statistical mechanics, which provides a simple and general framework for model reduction. I will discuss data-driven modeling and model reduction for chaotic / stochastic dynamical systems within this framework, highlighting some of the theoretical and practical issues that arise.

Short Bio Kevin K Lin is an Associate Professor of Mathematics at the University of Arizona.  He studied Computer Science and Mathematics at MIT and earned a PhD in Mathematics from UC Berkeley in 2003.  After an NSF Postdoctoral Fellowship at the Courant Institute, he joined the University of Arizona in 2007.  His current research interests include model reduction, data assimilation, Monte Carlo methods, and computational neuroscience.