1.2k citations · 3.3k across the 35 of their papers we have counts for
45 papers
A Koopman Operator-Based Prediction Algorithm and its Application to COVID-19 Pandemic
Igor Mezic, Zlatko Drmac, Nelida Crnjaric-Zic +6
The problem of prediction of behavior of dynamical systems has undergone a paradigm shift in the second half of the 20th century with the discovery of the possibility of chaotic dy…
A Transfer Operator Approach to Relativistic Quantum Wavefunction
Igor Mezic
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanic…
Algorithmic (Semi-)Conjugacy via Koopman Operator Theory
William T. Redman, Maria Fonoberova, Ryan Mohr +2
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a simila…
Koopman Reduced Order Modeling with Confidence Bounds
Ryan Mohr, Maria Fonoberova, Igor Mezic
This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spec…
An Operator Theoretic View on Pruning Deep Neural Networks
William T. Redman, Maria Fonoberova, Ryan Mohr +2
The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest. While many pruning methods have been developed…
Predicting the Critical Number of Layers for Hierarchical Support Vector Regression
Ryan Mohr, Maria Fonoberova, Zlatko Drmač +2
Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer…
Koopman Operator, Geometry, and Learning
Igor Mezic
We provide a framework for learning of dynamical systems rooted in the concept of representations and Koopman operators. The interplay between the two leads to the full description…
On Numerical Approximations of the Koopman Operator
Igor Mezic
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Lapl…
Koopman Resolvent: A Laplace-Domain Analysis of Nonlinear Autonomous Dynamical Systems
Yoshihiko Susuki, Alexandre Mauroy, Igor Mezic
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigro…
Applications of Koopman Mode Analysis to Neural Networks
Iva Manojlović, Maria Fonoberova, Ryan Mohr +4
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optim…
Spectral Analysis of the Koopman Operator for Partial Differential Equations
Hiroya Nakao, Igor Mezić
We provide an overview of the Koopman operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We i…
Control-Oriented, Data-Driven Models of Thermal Dynamics
Ljuboslav Boskic, Igor Mezic
Energy savings from efficiency methods in individual residential buildings are measured in 10's of dollars, while the energy savings from such measures nationally would amount to 1…
Exponentially decaying modes and long-term prediction of sea ice concentration using Koopman Mode Decomposition
James Hogg, Maria Fonoberova, Igor Mezic
Sea ice cover in the Arctic and Antarctic is an important indicator of changes in the climate, with important environmental, economic and security consequences. The complexity of t…
Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control
Carl Folkestad, Daniel Pastor, Igor Mezic +3
This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can…
Spectral analysis of mixing in 2D high-Reynolds flows
Hassan Arbabi, Igor Mezic
We use spectral analysis of Eulerian and Lagrangian dynamics to study the advective mixing in an incompressible 2D bounded cavity flow. A significant property of such a rotational…
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…