Our research focuses on the operator-theoretic approach to dynamical systems and applications in control, energy infrastructure and soft robotics. The application of Koopman operator methodology in this context enables data-driven learning of complex dynamical systems occurring in these applications. The framework that arise is versatile and can incorporate stochastic and hybrid elements of systems. Particular topics of interest include:

  • Developing methods for geometric analysis of state space in deterministic, non-smooth and stochastic systems,

  • Development of control-theoretic methodology in the Koopman framework,

  • Development of numerical methods for characterization of spectral properties of the Koopman operator,

  • Development of Koopman operator theory for partial differential equations, and

  • Application to modeling soft robotics systems


 

For more information on Dr. Igor Mezić, please refer to this interview by AMR Podcasts.

News

May 23 - 27, 2021 – SIAM Conference on Applications of Dynamical Systems (DS21)

In the Society for Industrial and Applied Mathematics (SIAM) conference on applied dynamical systems - DS21, held virtually due to COVID-19, experts and researchers from all over the world presented their recent findings in the area of applied mathematics and nonlinear dynamics. The Mezić research group from UCSB had a strong presence by unveiling their most recent discoveries...

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May 23, 2021 – Igor Mezić awarded J. D. Crawford Prize!

Igor Mezić receives the prestigious biennial J. D. Crawford Prize from the Society for Industrial and Applied Mathematics (SIAM) Activity Group on Dynamical Systems (SIAG/DS) for his innovative work on the use of the Koopman Operator in the analysis of dynamical systems. Igor's research and his recent success including this award is featured by an article on the ME website titled "Solving the Unsolvable".

Established in 2000, the ...

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March 12, 2021 – Postdoctoral researcher Ervin Kamenar joins the Mezić Group!

Ervin joins the Mezić research group as a Fulbright visiting scholar from the University of Rijeka (UNIRI), Faculty of Engineering, Croatia where he works in the Mechanical Engineering Department. Building upon the previous collaboration between UNIRI and UCSB research groups (developing Koopman-based control for nanometric positioning devices), Ervin will be working on the design, modeling, and control of a pneumatic soft robot arm by using Koopman operator methods.

The...

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March 10 - 12, 2021 – ARO MURI Review

Mezić research group reports on the 3rd year of research on the ARO MURI project "From Data-Driven Operator Theoretic Schemes to Prediction, Inference, and Control of Systems" on March 10 - 12, via a teleconference. The participants include researchers from Caltech, MIT, University of Michigan, University of Washington, and UCSB, as well as researchers from the Army Research Laboratory that are interested in the progress and outcomes of the programs. The successful completion of the first three years of the project has led to the award of...

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December 3, 2020 – Congratulations to Allan for successfully defending his PhD!

We are pleased to announce that Allan Avila has successfully defended his PhD Thesis “Theory and Applications of Pull-back Operators in Dynamical Systems”. 

September 22, 2019 – Michael Banks joins as a PhD

Michael received his B.S. and M.S. in aerospace engineering from the University of Illinois at Urbana-Champaign. Welcome Michael!

February 13, 2019 – Visiting researcher Corbinian Schlosser heads back to Austria

Corbinian, originally from Germany, is a mathematics Master's student studying at the University of Innsbruck in Austria. He has been with us since late summer 2018 and is now back at his home university to finish his Master's thesis. We'll miss you Corbi!

February 11 - 15, 2019 – Igor Mezić and colleagues host a workshop at IPAM

Igor Mezić, as part of an orgainizing committee including Didier Henrion (CNRS, LAAS), Senka Macesic (University of Rijeka), and Mihai Putinar (UCSB), hosted a workshop titled "Operator Theoretic Methods in Dynamic Data Analysis and Control" at the Institute for Pure and Applied Mathematics (IPAM) on the UCLA campus.

October 2018 – Postdoctoral researcher Milan Korda leaves the Mezić Group for new position

Milan has been with the Mezić Group since September of 2016 publishing seven papers as first author in that time! Milan is now a researcher at LAAS-CNRS in Toulouse, France. We'll miss you Milan!

September 24, 2018 – Congratulations to Nithin for successfully defending his PhD!

We are pleased to announce that Nithin Govindarajan has successfully defended his PhD Thesis "Periodic Approximations and Spectral Analysis of the Koopman Operator: Theory and Applications." 

August 21 - 22, 2018 – Mezić Group Hosts ARO MURI Combustion Conference

UC Santa Barbara welcomes government project leaders and researchers from around the country for two days to discuss and present new findings. Key speakers included Igor Mezić (UCSB), Beverley McKeon (Cal Tech), Yannis Kevrekidis (Princeton), Themis Sapsis (MIT), Steven Brunton (U Washington), and Shai Revzen (U Michigan).

January 15, 2018 – Congratulations to Hassan for successfully defending his PhD!

Hassan Arbabi successfully defended his PhD dissertation titled "Koopman Spectral Analysis and Mixing in Incompressible Flows". His dissertation will be soon available through ProQuest and the UCSB digitial library (Alexandria).

May 20, 2017 – Igor Mezić and his co-workers win a $6.25M DoD MURI award!

Igor Mezić is leading the team that won the 2017 MURI research award to initiate a project titled "From Data‐Driven Operator Theoretic Schemes to Prediction, Inference and Control of Systems". The award, which amounts to 6.25 million dollars, will fund researchers across UCSB, Caltech, University of Washington, University of Michigan and MIT. Igor's research and his recent success including this award is featured by an article on the ME website titled...

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May 21 - 25, 2017 – SIAM Conference on Applications of Dynamical Systems (DS17)

In the Society for Industrial and Applied Mathematics (SIAM) conference on applied dynamical systems - DS17, held at Snowbird, experts and researchers from all over the world presented their recent findings in the area of applied mathematics and nonlinear dynamics. The Mezić research group from UCSB had a strong presence by unveiling their most recent discoveries centered around Koopman-operator theoretic treatment of complex...

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