Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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The Mezic Research group is pleased to announce the PhD Dissertation Defense for Michael Georgescu

Date: Thursday, December 4, 2014
Time: 9:00am
Location: Materials Research Lab (MRL), Room 2048

Advisor: Prof. Igor Mezic
Title: Analysis of Systems in Buildings using Spectral Koopman Operator Methods

This work presents a viewpoint for analyzing data-based systems using an operator-theoretic approach based on the Koopman operator. In particular we focus on problems emerging from building systems analysis; a setting where systems are high-dimensional and described by large data-sets (either measured or generated from simulation), but for which equations describing the system often cannot be expressed analytically. In the building setting, natural cycles of operations exist that are driven by occupancy, plug load schedules and environmental conditions. Using properties of the Koopman operator, building data can be decomposed into spatial-temporal modes, and from these modes, characteristics of data can be studied at varying time-scales. In particular we present a variety of novel analysis techniques based on spectral properties of the Koopman operator that can be applied to a variety of applications ranging from the monitoring/visualization, model order reduction, and model calibration of building systems. Each chapter is dedicated to one specific application and the tools developed for it. Numerous examples are presented to illustrate the capabilities of the developed framework.

Last Updated on Wednesday, 03 December 2014 14:25

The Mezic Research Group is pleased to host C P Caulfield

We are pleased to have Dr Colm-cille P. Caulfield, from the University of Cambridge, visit the Mezic's research group this Tuesday, December 2, 2014.

Dr Colm-cille P. Caulfield is interested in fluid flows where density
variations play a critical dynamical role. He strives to use a combination
of mathematical modelling, numerical simulation and laboratory experimentation
to understand and pokies online quantify fundamental physical processes, particularly when
they are transient in nature.
Last Updated on Tuesday, 26 April 2016 15:27

Talk: Koopman Mode Decomposition, Mesohyperbolicity and Mixing

TUESDAY, OCTOBER 14, 2014 4:30 - 5:20

Igor Mezic (University of California, Santa Barbara (UC Santa Barbara))

Koopman Mode Decomposition, Mesohyperbolicity and Mixing

Los Angeles, California
Last Updated on Tuesday, 07 October 2014 17:33

Research Program Outline for Big Data Dynamics in Systems of Systems

Igor Mezić

The problem of design, reverse engineering and retrofitting for robust operation of large-scale interconnected dynamical systems is perhaps the engineering grand challenge of our time. Mathematics and engineering tools for treatment of individual components have been developed to a high degree of sophistication. However, when these components are connected - whether physically or by communication devices - new, collective phenomena can emerge that are not necessarily related to properties of individual components. The local consequences of such phenomena can be sensed - and the drive towards reduced cost and ubiquity of sensors leads to a massive amount of dynamically changing data. The phenomena indicated by sensed data have to be recognized, counteracted or perhaps even utilized dynamically in attempts to achieve optimal design and operation. Here are some of the critical elements of the applied problem at hand, the "Big Data Dynamics in Systems of Systems", and our viewpoint on the associated research directions.

Last Updated on Friday, 23 May 2014 12:54

The Mezic Research Group is pleased to host Kari Kuester

On the spectrum of a Koopman operator of a dynamical system

Kari Kuester

Department of Mathematics

University of Tuebingen, Germany

Engineering Building II, Room 2243

Wednesday, May 21, 2014

10:30 am - 11:30 am


The Koopman operator permits to linearize dynamical systems in a way that all important information of the original system is preserved. In particular it is interesting to study the eigenvalues and eigenfunctions of the Koopman operator. The so called Jacobs-Glicksberg-de Leeuw-splitting shows that unimodular eigenvalues are of particular interest. It decomposes the observable space into a structured and a random part. The structured part is spanned by the eigenfunctions corresponding to unimodular eigenvalues and gives insight into the longterm behavior of the Koopman operator.

Short bio:

Kari Kuester studies Mathematics at the University of Tuebingen, Germany. She is preparing her Master thesis on "The Koopman linearization of dynamical systems" under the supervision of Prof. Rainer Nagel and is currently working with Prof. Frank Neubrander at Louisiana State University, Baton Rouge.

Last Updated on Saturday, 31 May 2014 18:55

Review article "Applied Koopmanism" made the cover of AIP Chaos

An invited review article "Applied Koopmanism", co-written by M. Budisic, R. Mohr, and I. Mezic, has just been published in journal Chaos in the focus issue Fifty Years of Chaos: Applied and Theoretical. Additionally, one of the images from the article has been featured on the cover page of the special issue.

The PDF version is available from the Chaos website, while the pre-print can be downloaded from arXiv:1206.3164.

Reference: Applied Koopmanism, Marko Budisic, Ryan Mohr, and Igor Mezic, Chaos 22, 047510 (2012), DOI:10.1063/1.4772195

Last Updated on Wednesday, 09 January 2013 14:49

PNAS publishes article about Deepwater Horizon plumes

Proceedings of National Academy of Sciences has published a paper which establishes that the shape of underwater plumes, released by Deepwater Horizon spill, resembles underwater clouds, not rivers, as it was previously thought. This finding reconciles seemingly incongruent measurements of bacterial activity, seen by other researchers.

Our group has contributed in the analysis of hydromechanics of the Gulf, where study of mesohyperbolic structures of fluid flows from measured data played the central role. Coupling these results with Dave Valentine's insights about bacterial activity explained the motion of hydrocarbones after the oil spill. Paper is, among others, coauthored by Igor Mezic, postdoctoral researcher Sophie Loire, and Stefan Ivic, graduate student at University of Rijeka, who visited the group during summer 2011.


Last Updated on Sunday, 15 January 2012 10:49