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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…
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Milan Korda, Igor Mezić
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where…
Quasi-Periodic Intermittency in Oscillating Cylinder Flow
Bryan Glaz, Igor Mezic, Maria Fonoberova +1
Fluid dynamics induced by periodically forced flow around a cylinder is analyzed computationally for the case when the forcing frequency is much lower than the von K{á}rm{á}n vorte…
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…
Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport
Alexandre Fabregat, Igor Mezic, Andrew C. Poje
We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fiel…
Programmable Potentials: Approximate N-body potentials from coarse-level logic
Gunjan S. Thakur, Ryan Mohr, Igor Mezić
This paper gives a systematic method for constructing an N-body potential, approximating the true potential, that accurately captures meso-scale behavior of the chemical or biologi…