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Related papers: Model Reduction via Dynamic Mode Decomposition

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Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…

Signal Processing · Electrical Eng. & Systems 2020-12-16 Mohammad N. Murshed , M. Monir Uddin

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…

Dynamical Systems · Mathematics 2017-10-31 Naoya Takeishi , Yoshinobu Kawahara , Takehisa Yairi

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Dynamical Systems · Mathematics 2024-08-06 George Haller , Bálint Kaszás

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

Machine Learning · Computer Science 2025-07-03 Nikita Sakovich , Dmitry Aksenov , Ekaterina Pleshakova , Sergey Gataullin

Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM…

Numerical Analysis · Mathematics 2020-03-30 Hannah Lu , Daniel M. Tartakovsky

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

Numerical Analysis · Mathematics 2016-11-16 D. A. Bistrian , I. M. Navon

The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…

Computational Physics · Physics 2023-11-29 Yuhui Yin , Chenhui Kou , Shengkun Jia , Lu Lu , Xigang Yuan , Yiqing Luo

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

Numerical Analysis · Mathematics 2023-07-26 Jovan Žigić

We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…

Numerical Analysis · Mathematics 2023-06-28 Hannah Lu , Daniel M. Tartakovsky

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…

Systems and Control · Computer Science 2017-12-01 Zhe Bai , Eurika Kaiser , Joshua L. Proctor , J. Nathan Kutz , Steven L. Brunton

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

Numerical Analysis · Mathematics 2021-07-28 Hannah Lu , Daniel M. Tartakovsky

Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…

Systems and Control · Electrical Eng. & Systems 2025-08-05 Ziqin He , Mengqi Hu , Yifei Lou , Can Chen

The Dynamic Mode Decomposition (DMD) is a tool of trade in computational data driven analysis of fluid flows. More generally, it is a computational device for Koopman spectral analysis of nonlinear dynamical systems, with a plethora of…

Numerical Analysis · Mathematics 2017-08-10 Zlatko Drmač , Igor Mezić , Ryan Mohr

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

Signal Processing · Electrical Eng. & Systems 2021-10-26 Manu Krishnan , Serkan Gugercin , Pablo A. Tarazaga

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Numerical Analysis · Mathematics 2019-08-14 Stefan Klus , Patrick Gelß , Sebastian Peitz , Christof Schütte

Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as…

Machine Learning · Computer Science 2024-09-26 Konstantinos Kevopoulos , Dongwei Ye

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…

Fluid Dynamics · Physics 2023-02-01 Matthew J. Colbrook , Lorna J. Ayton , Máté Szőke

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…

Dynamical Systems · Mathematics 2024-12-04 Matthew J. Colbrook , Catherine Drysdale , Andrew Horning

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…

Fluid Dynamics · Physics 2017-08-02 Yuya Ohmichi

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

Dynamical Systems · Mathematics 2023-02-21 Minwoo Lee , Jongho Park