1.2k citations · 3.3k across the 35 of their papers we have counts for
17 papers · 1 filter
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…
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…
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…
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…
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…
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…
Koopman Operator Spectrum for Random Dynamical Systems
Nelida Črnjarić-Žic, Senka Maćešić, Igor Mezić
In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum…
Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
Hassan Arbabi, Igor Mezić
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-di…
An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
Nithin Govindarajan, Hassan Arbabi, Louis van Blargian +3
We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a…
Existence of invariant tori in three dimensional maps with degeneracy
Umesh Vaidya, Igor Mezic
We prove a KAM-type result for the persistence of two-dimensional invariant tori in perturbations of integrable action-angle-angle maps with degeneracy, satisfying the intersection…
Extreme phase sensitivity in systems with fractal isochrons
Alexandre Mauroy, Igor Mezic
Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this co…
Global stability analysis using the eigenfunctions of the Koopman operator
Alexandre Mauroy, Igor Mezic
We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can…
Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
Alexandre Mauroy, Igor Mezic, Jeff Moehlis
For asymptotically periodic systems, a powerful (phase) reduction of the dynamics is obtained by computing the so-called isochrons, i.e. the sets of points that converge toward the…
Applied Koopmanism
Marko Budišić, Ryan M. Mohr, Igor Mezić
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincaré's geometric picture that focuses on "dynamics of states". While this p…