Koopman Theory for Partial Differential Equations

Hamiltonian systems and transformation in Hilbert space

B. O. Koopman · 1931

Earlier work this paper cites.

Dynamical systems of continuous spectra

B. O. Koopman and J. V. Neumann · 1932

Earlier work this paper cites.

A mathematical model illustrating the theory of turbulence

J. M. Burgers · 1948

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The partial differential equation u t + u ​ u x = μ ​ u x ​ x u_{t}+uu_{x}=\mu u_{xx}

E. Hopf · 1950

Earlier work this paper cites.

On a quasi-linear parabolic equation occurring in aerodynamics

J. D. Cole · 1951

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

W.-H. Steeb and F. Wilhelm · 1980

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Nonlinear dynamical systems and Carleman linearization

K. Kowalski, W.-H. Steeb, and K. Kowalksi · 1991

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Infinite-dimensional carleman linearization, the lie series and optimal control of non-linear partial differential equations

S. P. Banks · 1992

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A tutorial on support vector machines for pattern recognition

C. J. Burges · 1998

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Kernel-based methods and function approximation

G. Baudat and F. Anouar · 2001

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Comparison of systems with complex behavior

I. Mezić and A. Banaszuk · 2004

Cited alongside, same era.

A kernel view of the dimensionality reduction of manifolds

S. Mika J. Ham, D. D. Lee and B. Schölkopf · 2004

Cited alongside, same era.

Spectral properties of dynamical systems, model reduction and decompositions

I. Mezić · 2005

Cited alongside, same era.

Dynamic mode decomposition of numerical and experimental data

P. J. Schmid and J. Sesterhenn · 2008

Cited alongside, same era.

Kernel methods in machine learning

B. Schölkopf T. Hofmann and A. Smola · 2008

Cited alongside, same era.

Spectral analysis of nonlinear flows

C. W. Rowley, I. Mezić, S. Bagheri, P. Schlatter, and D.S. Henningson · 2009

Cited alongside, same era.

Analysis of fluid flows via spectral properties of the Koopman operator

I. Mezić · 2013

Later among the works it cites.

On dynamic mode decomposition: theory and applications

J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014

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Dynamic mode decomposition and the Koopman operator: algorithms and applications

C. W. Rowley, M. O. Williams, and I. G. Kevrekidis · 2014

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A kernel approach to data-driven Koopman spectral analysis

Original

M. O. Williams, C. W. Rowley, and I. G. Kevrekidis · 2014

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Closed-loop turbulence control: Progress and challenges

S. L. Brunton and B. R. Noack · 2015

Later among the works it cites.

A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition