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Prediction Accuracy of Dynamic Mode Decomposition
SIAM Journal on Scientific Computing, 2020 Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression. While multiple numerical tests demonstrated the power and efficiency of DMD in representing data (i.e., in the interpolation mode), applications of DMD as a predictive tool (i.e., in the extrapolation mode) are scarce.
Hannah Lu, Daniel M. Tartakovsky
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Bayesian Dynamic Mode Decomposition [PDF]
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017 Dynamic mode decomposition (DMD) is a data-driven method for calculating a modal representation of a nonlinear dynamical system, and it has been utilized in various fields of science and engineering. In this paper, we propose Bayesian DMD, which provides a principled way to transfer the advantages of the Bayesian formulation into DMD.
Naoya Takeishi +3 more
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Optimal low-rank Dynamic Mode Decomposition [PDF]
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASPP), New Orleans, USA ...
Héas, Patrick, Herzet, Cédric
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Dynamic Mode Decomposition with Control Liouville Operators
IFAC-PapersOnLine, 2021 This paper builds the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville operators and control occupation kernels are introduced to separate the drift dynamics from the input dynamics.
Joel A. Rosenfeld +1 more
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Tensor Train-Based Higher-Order Dynamic Mode Decomposition for Dynamical Systems
Mathematics, 2023 Higher-order dynamic mode decomposition (HODMD) has proved to be an efficient tool for the analysis and prediction of complex dynamical systems described by data-driven models.
Keren Li, Sergey Utyuzhnikov
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Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis [PDF]
, 2018 We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to modes that each ...
Colonius, Tim +2 more
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Dynamic mode decomposition of numerical data in natural circulation
Brazilian Journal of Radiation Sciences, 2021 Dynamic mode decomposition (DMD) has been used for experimental and numerical data analysis in fluid dynamics. Despite of its advantages, the application of the DMD methodology to investigate the natural circulation in nuclear reactors are very scarce in
José Luiz Horacio Faccini
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Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition
Mathematics, 2022 Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD.
Jan Heiland, Benjamin Unger
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Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation [PDF]
, 2005 Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass transition, leading to
A. Vrij +13 more
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Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition
MathematicsSpatio-temporal dynamic mode decomposition (STDMD) is an extension of dynamic mode decomposition (DMD) designed to handle spatio-temporal datasets. It extends the framework so that it can analyze data that have both spatial and temporal variations.
Gyurhan Nedzhibov
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