DMS Colloquium: Kevin Lin

Speaker: Kevin K Lin, College of Mathematical Sciences, University of Arizona

Title: Mori--Zwanzig formalism and discrete-time modeling of chaotic dynamics


Abstract: Nonlinear dynamic phenomena often require a large number of dynamical variables to model, only a small fraction of which are of direct interest.  Reduced models that use only the relevant dynamical variables can be very useful in such situations, both for computational efficiency and insights into the dynamics.  Recent work has shown that the NARMAX (Nonlinear Auto-Regressive Moving-Average with eXogenous inputs) representation of stochastic processes provides an effective basis for parametric model reduction in a number of concrete settings [Chorin-Lu PNAS 2015].  In this talk, I will review these developments as well as a general theoretical framework for model reduction due to Mori and Zwanzig.  I will then explain how the NARMAX method can be seen as a special case of the Mori-Zwanzig formalism and discuss some general implications and technical issues that arise.  These ideas will be illustrated on a prototypical model of spatiotemporal chaos.

Faculty host: Xiaoying Han