479 citations · 691 across the 11 of their papers we have counts for
12 papers
Invariant Consistent Dynamic Mode Decomposition
Gowtham S Seenivasaharagavan, Milan Korda, Hassan Arbabi +1
Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-c…
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…
Coarse-grained and emergent distributed parameter systems from data
Hassan Arbabi, Felix P. Kemeth, Tom Bertalan +1
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) fro…
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Hassan Arbabi, Judith E. Bunder, Giovanni Samaey +2
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural…
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…
Generative stochastic modeling of strongly nonlinear flows with non-Gaussian statistics
Hassan Arbabi, Themistoklis Sapsis
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial a…
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…
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…
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.…
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…
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…