Modern Koopman Theory for Dynamical Systems
type: Item
instance of: scholarly article
title: Modern Koopman Theory for Dynamical Systems
zbMATH Open document ID: 1497.37105
DOI: 10.1137/21M1401243
author: S. L. Brunton
author: Marko Budišić
author: Eurika Kaiser
author: J. N. Kutz
published in: SIAM Review
publication date: 2022-05-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/2102.12086
Mathematics Subject Classification ID: 37M99
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37N35
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 7525524
zbMATH Keywords: dynamical systems
zbMATH Keywords: Koopman operator
zbMATH Keywords: data-driven discovery
zbMATH Keywords: control theory
zbMATH Keywords: spectral theory
zbMATH Keywords: operator theory
zbMATH Keywords: dynamic mode decomposition
zbMATH Keywords: embeddings
describes a project that uses: DeepONet
describes a project that uses: PyDMD
describes a project that uses: rsvd
describes a project that uses: VAMPnets
describes a project that uses: odmd
describes a project that uses: GAIO
describes a project that uses: EnKF
describes a project that uses: LANDO
MaRDI profile type: Publication
arXiv ID: 2102.12086
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Q3925229
cites work: Manifolds, tensor analysis, and applications.
cites work: Model and data reduction for data assimilation: particle filters employing projected forecasts and data with application to a shallow water model
cites work: An incremental approach to online dynamic mode decomposition for time-varying systems with applications to EEG data modeling
cites work: Resonances and the extension of dynamics to rigged Hilbert spaces
cites work: Generalized spectral decomposition and intrinsic irreversibility of the Arnold cat map
cites work: Data assimilation: Mathematical and statistical perspectives
cites work: Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
cites work: Q4210478
cites work: Variable Projection Methods for an Optimized Dynamic Mode Decomposition
cites work: Spectral characterization of WienerWintner dynamical systems
cites work: Consistent Dynamic Mode Decomposition
cites work: Koopman-mode decomposition of the cylinder wake
cites work: Infinite-dimensional Carleman linearization, the Lie series and optimal control of non-linear partial differential equations
cites work: Learning data-driven discretizations for partial differential equations
cites work: Sparse identification of multiphase turbulence closures for coupled fluid–particle flows
cites work: Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
cites work: A survey of projection-based model reduction methods for parametric dynamical systems
cites work: On reduced input-output dynamic mode decomposition
cites work: Pseudogenerators of Spatial Transfer Operators
cites work: Geometric considerations of a good dictionary for Koopman analysis of dynamical systems: cardinality, ``primary eigenfunction,'' and efficient representation
cites work: On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions
cites work: Applied and computational measurable dynamics
cites work: Q4862306
cites work: Statistical modeling: The two cultures. (With comments and a rejoinder).
cites work: Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements
cites work: Volterra series and geometric control theory
cites work: Q3596129
cites work: Time-series analysis
cites work: Discovering governing equations from data by sparse identification of nonlinear dynamical systems
cites work: Data-Driven Science and Engineering
cites work: Machine Learning for Fluid Mechanics
cites work: Compressed sensing and dynamic mode decomposition
cites work: Compressive Sensing and Low-Rank Libraries for Classification of Bifurcation Regimes in Nonlinear Dynamical Systems
cites work: Geometry of the ergodic quotient reveals coherent structures in flows
cites work: Applied Koopmanism
cites work: Kernel Analog Forecasting: Multiscale Test Problems
cites work: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
cites work: Applied Nonautonomous and Random Dynamical Systems
cites work: Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires
cites work: Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
cites work: Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part I: Theory

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses

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cites work: Q4258125

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Diffusion maps

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: On a quasi-linear parabolic equation occurring in aerodynamics

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: The dynamics of control. With an appendix by Lars Grüne

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Q3955608

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Koopman operator spectrum for random dynamical systems

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Delay-coordinate maps and the spectra of Koopman operators

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Koopman spectra in reproducing kernel Hilbert spaces

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Reproducing kernel Hilbert space compactification of unitary evolution groups

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Q4544293

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: A subdivision algorithm for the computation of unstable manifolds and global attractors

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Exploring invariant sets and invariant measures

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: On the Approximation of Complicated Dynamical Behavior

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: On the Koopman Operator of Algorithms

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Compressed sensing

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: A new selection operator for the discrete empirical interpolation method -- improved a priori error bound and extensions

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cites work: Data Driven Modal Decompositions: Analysis and Enhancements

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cites work: Data Driven Koopman Spectral Analysis in Vandermonde--Cauchy Form via the DFT: Numerical Method and Theoretical Insights

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cites work: On Least Squares Problems with Certain Vandermonde--Khatri--Rao Structure with Applications to DMD

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cites work: Experimental investigation of nonlinear instabilities in annular liquid sheets

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cites work: Turbulence Modeling in the Age of Data

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cites work: Ergodic theory of chaos and strange attractors

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cites work: Operator Theoretic Aspects of Ergodic Theory

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cites work: Global linearization and fiber bundle structure of invariant manifolds

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Randomized Dynamic Mode Decomposition

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cites work: The ensemble Kalman filter for combined state and parameter estimation

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cites work: Computing Lagrangian coherent structures from their variational theory

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cites work: Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles

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cites work: Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools

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cites work: A trajectory-free framework for analysing multiscale systems

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cites work: Estimating Long-Term Behavior of Flows without Trajectory Integration: The Infinitesimal Generator Approach

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cites work: Escape rates and Perron-Frobenius operators: open and closed dynamical systems

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cites work: Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

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cites work: Model predictive control: Theory and practice - a survey

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cites work: Chaos, Scattering and Statistical Mechanics

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cites work: Data-driven spectral decomposition and forecasting of ergodic dynamical systems

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cites work: Delay-coordinate maps, coherence, and approximate spectra of evolution operators

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cites work: Extraction and prediction of coherent patterns in incompressible flows through space-time koopman analysis

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cites work: Deep learning models for global coordinate transformations that linearise PDEs

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cites work: On the Approximation of Koopman Spectra for Measure Preserving Transformations

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cites work: Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction

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cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

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cites work: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

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cites work: Lagrangian coherent structures from approximate velocity data

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cites work: Approximation Theories for Measure Preserving Transformations

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cites work: Nonlinear controllability and observability

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cites work: Data-driven resolvent analysis

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cites work: Centering Data Improves the Dynamic Mode Decomposition

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cites work: Zero-dimensional singular continuous spectrum for smooth differential equations on the torus

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cites work: Turbulence, Coherent Structures, Dynamical Systems and Symmetry

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cites work: The partial differential equation ut + uux = μxx

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cites work: Data-driven nonlinear stabilization using Koopman operator

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cites work: Sufficient conditions for controllability

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cites work: An Introduction to Statistical Learning

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cites work: From Bypass Transition to Flow Control and Data-Driven Turbulence Modeling: An Input–Output Viewpoint

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cites work: Componentwise energy amplification in channel flows

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cites work: Q4848216

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cites work: An eigensystem realization algorithm for modal parameter identification and model reduction

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cites work: Identification of observer/Kalman filter Markov parameters - Theory and experiments

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cites work: The rate of convergence in ergodic theorems

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cites work: Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

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cites work: Data-driven approximations of dynamical systems operators for control

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cites work: Sparsity enabled cluster reduced-order models for control

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cites work: Mathematical Description of Linear Dynamical Systems

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cites work: Time-Delay Observables for Koopman: Theory and Applications

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cites work: Q3412607

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cites work: APPROXIMATIONS IN ERGODIC THEORY

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cites work: Q3091758

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cites work: Tensor-based dynamic mode decomposition

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cites work: On the numerical approximation of the Perron-Frobenius and Koopman operator

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cites work: Data-driven model reduction and transfer operator approximation

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cites work: Data-driven approximation of the Koopman generator: model reduction, system identification, and control

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cites work: Eigendecompositions of transfer operators in reproducing kernel Hilbert spaces

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cites work: Singular continuous spectrum and quantitative rates of weak mixing

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cites work: Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics

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cites work: Dynamical Systems of Continuous Spectra

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cites work: Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: On convergence of extended dynamic mode decomposition to the Koopman operator

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cites work: Optimal Construction of Koopman Eigenfunctions for Prediction and Control

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cites work: Data-driven spectral analysis of the Koopman operator

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cites work: Q4002304

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cites work: Sparse Sensing and DMD-Based Identification of Flow Regimes and Bifurcations in Complex Flows

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cites work: Deep learning in fluid dynamics

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cites work: Q2957673

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cites work: Multiresolution dynamic mode decomposition

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems

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cites work: Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits

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cites work: Linearization in the large of nonlinear systems and Koopman operator spectrum

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cites work: Q4998931

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cites work: Chaos, fractals, and noise: Stochastic aspects of dynamics.

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cites work: Data Assimilation

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cites work: Q4531961

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cites work: Integrals of nonlinear equations of evolution and solitary waves

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Approximation of measure preserving transformations

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cites work: Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

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cites work: Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

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cites work: Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

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cites work: Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture

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cites work: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

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cites work: Q4724470

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cites work: Estimating the domain of attraction of nonlinear feedback systems

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cites work: The Lorenz attractor is mixing

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cites work: Reduced-order models for control of fluids using the eigensystem realization algorithm

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cites work: Koopman operator theory for nonautonomous and stochastic systems

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cites work: Koopman Operator Family Spectrum for Nonautonomous Systems

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cites work: The role of the rigged Hilbert space in quantum mechanics

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Q4532409

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Physics constrained nonlinear regression models for time series

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cites work: Conceptual dynamical models for turbulence

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cites work: Dynamic mode decomposition for financial trading strategies

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cites work: Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns

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cites work: Optimized Sampling for Multiscale Dynamics

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cites work: Q3275105

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cites work: Data-driven Koopman operator approach for computational neuroscience

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cites work: Subgrid modelling for two-dimensional turbulence using neural networks

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cites work: Koopman-Based Lifting Techniques for Nonlinear Systems Identification

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cites work: On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics

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cites work: Global Stability Analysis Using the Eigenfunctions of the Koopman Operator

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cites work: Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics

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cites work: The Koopman Operator in Systems and Control

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cites work: A critical-layer framework for turbulent pipe flow

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Q5424098

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Spectral properties of dynamical systems, model reduction and decompositions

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Analysis of Fluid Flows via Spectral Properties of the Koopman Operator

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Spectrum of the Koopman operator, spectral expansions in functional spaces, and state-space geometry

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Comparison of systems with complex behavior

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Uncertainty propagation in dynamical systems

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: A method for visualization of invariant sets of dynamical systems based on the ergodic partition

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Ergodic theorem, ergodic theory, and statistical mechanics

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cites work: Q5446760

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cites work: Carleman Linearization of Linearly Observable Polynomial Systems

Modern Koopman Theory for Dynamical Systems (cites work)
cites work: Flow structures around a high-speed train extracted using proper orthogonal decomposition and dynamic mode decomposition

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cites work: Mode decomposition on surface-mounted cube

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cites work: Q3940056

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cites work: Diffusion maps, spectral clustering and reaction coordinates of dynamical systems

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cites work: Spectral analysis of the Koopman operator for partial differential equations

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cites work: Proof of the Quasi-Ergodic Hypothesis

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cites work: Zur Operatorenmethode in der klassischen Mechanik

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cites work: Recursive dynamic mode decomposition of transient and post-transient wake flows

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cites work: A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems

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cites work: Tensor-based computation of metastable and coherent sets

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cites work: Q3993068

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cites work: Linearly Recurrent Autoencoder Networks for Learning Dynamics

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cites work: Koopman mode expansions between simple invariant solutions

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cites work: Sparsity-promoting algorithms for the discovery of informative Koopman-invariant subspaces

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cites work: Koopman Analysis of Isolated Fronts and Solitons

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cites work: Data-driven operator inference for nonintrusive projection-based model reduction

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cites work: Koopman operator-based model reduction for switched-system control of PDEs

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cites work: Feedback control of nonlinear PDEs using data-efficient reduced order models based on the Koopman operator

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cites work: Data-Driven Model Predictive Control using Interpolated Koopman Generators

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cites work: Q4715203

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cites work: Linear system identification via an asymptotically stable observer

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cites work: On the rate of mixing of Axiom A flows

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cites work: Dynamic mode decomposition with control

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cites work: Generalizing Koopman Theory to Allow for Inputs and Control

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cites work: Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems

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cites work: Substitution dynamical systems. Spectral analysis

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cites work: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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cites work: Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

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cites work: On Koopman mode decomposition and tensor component analysis

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cites work: Q4185363

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cites work: Q3909512

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cites work: Selected topics from the metric theory of dynamical systems

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cites work: Dynamic mode decomposition for continuous time systems with the Liouville operator

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cites work: Spectral analysis of nonlinear flows

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cites work: Koopman operator and its approximations for systems with symmetries

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cites work: Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems

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cites work: Dynamic mode decomposition of numerical and experimental data

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cites work: Estimation of the Koopman Generator by Newton's Extrapolation

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cites work: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

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cites work: On robust computation of Koopman operator and prediction in random dynamical systems

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cites work: Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics

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cites work: Non-linear autonomous systems of differential equations and Carleman linearization procedure

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cites work: Fourier asymptotics of fractal measures

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cites work: Rigged Hilbert spaces for chaotic dynamical systems

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cites work: Invariant Sets in Quasiperiodically Forced Dynamical Systems

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cites work: Coherent swing instability of power grids

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cites work: Q3658782

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cites work: A set oriented definition of finite-time Lyapunov exponents and coherent sets

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cites work: Q4864293

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cites work: Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis

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cites work: Hydrodynamic Stability Without Eigenvalues

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cites work: On dynamic mode decomposition: theory and applications

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cites work: The Future of Data Analysis

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cites work: Q3259049

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cites work: Actuator and sensor placement in linear advection PDE with building system application

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cites work: 4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems

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cites work: Q4366804

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cites work: Harmonic Analysis and Ergodic Theory

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cites work: Introduction to Applied Nonlinear Dynamical Systems and Chaos

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cites work: A data-driven approximation of the koopman operator: extending dynamic mode decomposition

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cites work: A kernel-based method for data-driven Koopman spectral analysis

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cites work: A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems

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cites work: Variational approach for learning Markov processes from time series data

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cites work: Online Dynamic Mode Decomposition for Time-Varying Systems

Modern Koopman Theory for Dynamical Systems (OpenAlex ID)
OpenAlex ID: W3129637124