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


 

Dr. Igor Mezić's article in the Notices of the American Mathematical Society describing the role of the Koopman operator in learning of dynamical systems.


 

               Dr. Igor Mezić's talk at SIAM DS21:

  Koopman Operator, Geometry, and Learning of Dynamical Systems


 

Dr. Igor Mezić's talk at the Scientific Computing and Artificial Intelligence (SCAI) Laboratory at Notre Dame:

     Koopman Operator Theory for Dynamical Systems, Control and Data Analytics

 

Dr. Igor Mezić's interview with AMR Podcasts.


 

News

May 20 and June 3, 2022  – The Mezić Group is pleased to host Allan Avila from AIMdyn Inc.

Allan Avila from AIMdyn Inc., USA will give a Zoom seminar on May 20 and June 3, 2022 at 9AM PST.

Title: Spectral Properties of Pullback Operators on Vector Bundles of a Dynamical System

Abstract: The spectrum of the Koopman operator has been shown to encode many important statistical and geometric properties of a dynamical system. In this talk, we consider induced linear...

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January 3, 2022 – Alan Cao graduates with Master's

Alan graduated from UCSB in 2018 with a B.S. in Electrical Engineering. He has officially finished his M.S. in Electrical and Computer Engineering from UCSB in Winter 2022. Congratulations Alan!

December 12 - 15, 2022 – Igor Mezić will be co-chairing the 2022 International Symposium on Nonlinear Theory and Its Applications (NOLTA2022)

The 2022 International Symposium on Nonlinear Theory and Its Applications - NOLTA2022, will be held at Conference Park 25/7, Opatija, Croatia, December 12th-15th, 2022. The objective of the symposium is to provide a forum for exchanges of the latest results related to...

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

Recordings of our talks are on our Youtube channel linked below.

In the Society for Industrial and Applied Mathematics (SIAM) conference on applied dynamical systems - DS21, held virtually due to COVID-19, experts and researchers...

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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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