Past Applied Dynamical Systems and Inverse Problems Seminar

24 February 2015
11:00
to
12:30
Visiting Professor Boumediene Hamzi
Abstract

Abstract: We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control and random dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems -with a reasonable expectation of success - once the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. In particular, we develop computable, non-parametric estimators approximating controllability and observability energy/Lyapunov functions for nonlinear systems, and study the ellipsoids they induce. It is then shown that the controllability energy estimator provides a key means for approximating the invariant measure of an ergodic, stochastically forced nonlinear system. We also apply this approach to the problem of model reduction of nonlinear control systems.

In all cases the relevant quantities are estimated from simulated or observed data. These results collectively argue that there is a reasonable passage from linear dynamical systems theory to a data-based nonlinear dynamical systems theory through reproducing kernel Hilbert spaces. This is a joint work with J. Bouvrie (MIT).

  • Applied Dynamical Systems and Inverse Problems Seminar
3 June 2014
11:00
Dr Peter Dueben
Abstract
Inexact hardware trades reduced numerical precision against a reduction in computational cost. A reduction of computational cost would allow weather and climate simulations at higher resolution. In the first part of this talk, I will introduce the concept of inexact hardware and provide results that show the great potential for the use of inexact hardware in weather and climate simulations. In the second part of this talk, I will discuss how rounding errors can be assessed if the forecast uncertainty and the chaotic behaviour of the atmosphere is acknowledged. In the last part, I will argue that rounding errors do not necessarily degrade numerical models, they can actually be beneficial. This conclusion will be based on simulations with a model of the one-dimensional Burgers' equation.
  • Applied Dynamical Systems and Inverse Problems Seminar

Pages