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On least squares problems with certain Vandermonde--Khatri--Rao structure with applications to DMD
Zlatko Drmač, Igor Mezić, Ryan Mohr
This paper proposes a new computational method for solving structured least squares problems that arise in the process of identification of coherent structures in fluid flows. It i…
Optimal construction of Koopman eigenfunctions for prediction and control
Milan Korda, Igor Mezić
This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of…
Data driven Koopman spectral analysis in Vandermonde-Cauchy form via the DFT: numerical method and theoretical insights
Zlatko Drmač, Igor Mezić, Ryan Mohr
The goals and contributions of this paper are twofold. It provides a new computational tool for data driven Koopman spectral analysis by taking up the formidable challenge to devel…
Prandtl-Batchelor theorem for flows with quasi-periodic time dependence
Hassan Arbabi, Igor Mezić
The classical Prandtl-Batchelor theorem (Prandtl 1904; Batchelor 1956) states that in the regions of steady 2D flow where viscous forces are small and streamlines are closed, the v…
Invariant Sets in Quasiperiodically Forced Dynamical Systems
Yoshihiko Susuki, Igor Mezić
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preservi…
Spectral Complexity of Directed Graphs and Application to Structural Decomposition
Igor Mezić, Vladimir A. Fonoberov, Maria Fonoberova +1
We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts.…
Convex computation of extremal invariant measures of nonlinear dynamical systems and Markov processes
Milan Korda, Didier Henrion, Igor Mezic
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The se…
A data-driven Koopman model predictive control framework for nonlinear flows
Hassan Arbabi, Milan Korda, Igor Mezic
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.…
Global computation of phase-amplitude reduction for limit-cycle dynamics
A. Mauroy, I. Mezic
Recent years have witnessed increasing interest to phase-amplitude reduction of limit-cycle dynamics. Adding an amplitude coordinate to the phase coordinate allows to take into acc…
On the approximation of Koopman spectra for measure preserving transformations
Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran +1
For the class of continuous, measure-preserving automorphisms on compact metric spaces, a procedure is proposed for constructing a sequence of finite-dimensional approximations to…