244 citations · 802 across the 18 of their papers we have counts for
20 papers
Beyond Invariant Dictionary: Data-Driven Koopman Spectral Recovery with Filtered Extended Dynamic Mode Decomposition
Siji Chen, Igor Mezić, Sui Tang
The Koopman operator provides a linear framework for analyzing nonlinear dynamical systems through spectral properties. Extended Dynamic Mode Decomposition (EDMD) approximates this…
Clarifying the effect of mean subtraction on Dynamic Mode Decomposition
Gowtham S Seenivasaharagavan, Milan Korda, Hassan Arbabi +1
Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven ap…
Modeling, Reduction, and Control of a Helically Actuated Inertial Soft Robotic Arm via the Koopman Operator
David A. Haggerty, Michael J. Banks, Patrick C. Curtis +2
Soft robots promise improved safety and capability over rigid robots when deployed in complex, delicate, and dynamic environments. However, the infinite degrees of freedom and high…
Robust Approximation of the Stochastic Koopman Operator
Mathias Wanner, Igor Mezić
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or obs…
From unsteady to quasi-steady dynamics in the streamwise-oscillating cylinder wake
Maysam Shamai, Scott T. M. Dawson, Igor Mezić +1
The flow around a cylinder oscillating in the streamwise direction with a frequency, , much lower than the shedding frequency, , has been relatively less studied than the…
Search strategy in a complex and dynamic environment: the MH370 case
Stefan Ivić, Bojan Crnković, Hassan Arbabi +3
Search and detection of objects on the ocean surface is a challenging task due to the complexity of the drift dynamics and lack of known optimal solutions for the path of the searc…
On Learning Hamiltonian Systems from Data
Tom Bertalan, Felix Dietrich, Igor Mezić +1
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on re…
On the approximation of Koopman spectra of measure-preserving flows
Nithin Govindarajan, Ryan Mohr, Shivkumar Chandrasekaran +1
The method of using periodic approximations to compute the spectral decomposition of the Koop- man operator is generalized to the class of measure-preserving flows on compact metri…
Power grid transient stabilization using Koopman model predictive control
Milan Korda, Yoshihiko Susuki, Igor Mezić
This work addresses the problem of transient stabilization of a power grid, following a destabilizing disturbance. The model considered is the cascade interconnection of seven New…
Data-driven spectral analysis of the Koopman operator
Milan Korda, Mihai Putinar, Igor Mezić
Starting from measured data, we develop a method to compute the fine structure of the spectrum of the Koopman operator with rigorous convergence guarantees. The method is based on…
Koopman Spectrum for Cascaded Systems
Ryan Mohr, Igor Mezić
This paper considers the evolution of Koopman principal eigenfunctions of cascaded dynamical systems. If each component subsystem is asymptotically stable, the matrix norms of the…
Study of dynamics in post-transient flows using Koopman mode decomposition
Hassan Arbabi, Igor Mezić
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study t…
Koopman principle eigenfunctions and linearization of diffeomorphisms
Ryan Mohr, Igor Mezić
This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the conne…
On the correspondence between Koopman mode decomposition, resolvent mode decomposition, and invariant solutions of the Navier-Stokes equations
Ati S. Sharma, Igor Mezić, Beverley J. McKeon
The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rest…
Mesochronic classification of trajectories in incompressible 3D vector fields over finite times
Marko Budišić, Stefan Siegmund, Doan Thai Son +1
The mesochronic velocity is the average of the velocity field along trajectories generated by the same velocity field over a time interval of finite duration. In this paper we clas…
Data Fusion via Intrinsic Dynamic Variables: An Application of Data-Driven Koopman Spectral Analysis
Matthew O. Williams, Clarence W. Rowley, Igor Mezić +1
We demonstrate that numerically computed approximations of Koopman eigenfunctions and eigenvalues create a natural framework for data fusion in applications governed by nonlinear e…
Construction of eigenfunctions for scalar-type operators via Laplace averages with connections to the Koopman operator
Ryan Mohr, Igor Mezić
This paper extends Yosida's mean ergodic theorem in order to compute projections onto non-unitary eigenspaces for spectral operators of scalar-type on locally convex linear topolog…
Frontiers of chaotic advection
Hassan Aref, John R. Blake, Marko Budišić +20
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid…
Geometry of the ergodic quotient reveals coherent structures in flows
Marko Budišić, Igor Mezić
Dynamical systems that exhibit diverse behaviors can rarely be completely understood using a single approach. However, by identifying coherent structures in their state spaces, i.e…
Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets
Zoran Levnajić, Igor Mezić
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs…