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Dynamic Mode Decomposition : Data-Driven Modeling of Complex Systems

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SIAM, (2016)

Аннотация

The integration of data and scientific computation is driving a paradigm shift across the engineering, natural, and physical sciences. Indeed, there exists an unprecedented availability of high-fidelity measurements from time-series recordings, numerical simulations, and experimental data. When coupled with readily available algorithms and innovations in machine (statistical) learning, it is possible to extract meaningful spatio-temporal patterns that dominate dynamic activity. The focus of this book is on the emerging method of dynamic mode decomposition (DMD). DMD is a matrix decomposition technique that is highly versatile and builds upon the power of the singular value decomposition (SVD). The low-rank structures extracted from DMD are associated with temporal features as well as correlated spatial activity, thus providing a powerful diagnostic for state estimation, model building, control and prediction.

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  • @gdmcbain
    5 лет назад (последнее обновление5 лет назад)
    This timely book unfortunately contains a number of grotesque errors: * The Galerkin method does not require an orthogonal basis. (Section 2.1.4) * The eigenvalues of the conjugate transpose of a matrix are the complex conjugates of the eigenvalues of the matrix, regardless of whether the matrix is self-adjoint. (Section 3.1.1) One cannot approve of ch. 4 which heralds 'a transformative improvement in performance that is ideal for video surveillance and recognition applications'.
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