This is a critically important new direction because the governing equations of many problems Data-Driven Modeling of Complex Systems.

Nathan Kutz , Steven L. Brunton , Bingni W.

Brunton , Joshua L. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known.

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Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition DMD is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning.

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Data-Driven Modeling of Complex Systems , the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.

Nathan Kutz, Steven L.

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Data-Driven Modeling of Complex Systems J. Rowley Chapter Cited columns compressed DMD compressed sensing compute DMD constructed cylinder wake data matrix differential equations dimensional dimensionality reduction discrete-time DMD algorithm DMD eigenvalues DMD method DMD modes DMD spectrum DMDc dynamic mode decomposition eigenfunctions eigenvectors equation-free example extended DMD extract flow Fourier transform frame frequency function Hankel matrix high-dimensional hot spot infinite-dimensional inner product inputs J.

Kutz Journal kernel DMD kernel trick Koopman operator linear dynamical system low-dimensional low-rank machine learning Markov mathematical measurements mode amplitudes mp,mf mrDMD neural noise nonlinear dynamical nonlinear dynamical system number of snapshots observables optimal oscillations panel parameter pixels plot power spectrum prediction principal component proper orthogonal decomposition pseudoinverse reconstruction regression RPCA sampling window set gca signal simulation singular values solution space sparse spatial spatiotemporal spectral strategies subspace system identification techniques tion trading truncation variables vector wavelet.

Proctor SIAM , 23 nov.