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A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…

Machine Learning · Computer Science 2021-11-09 Sudam Surasinghe , Erik M. Bollt

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

Machine Learning · Computer Science 2021-05-11 Gabriel F. Barros , Malú Grave , Alex Viguerie , Alessandro Reali , Alvaro L. G. A. Coutinho

One of the central challenge for extracting governing principles of dynamical system via Dynamic Mode Decomposition (DMD) is about the limit data availability or formally called as Limited Data Acquisition in the present paper. In the…

Dynamical Systems · Mathematics 2024-08-31 Himanshu Singh

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

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Numerical Analysis · Mathematics 2022-04-21 Hannah Lu , Daniel M. Tartakovsky

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

Numerical Analysis · Mathematics 2020-11-24 Ion Victor Gosea , Igor Pontes Duff

We present an extension of optimal mode decomposition (OMD) for autonomous systems to systems with controls. The extension is developed along the same lines as the extension of dynamic mode decomposition (DMD) to DMD with control (DMDc).…

Optimization and Control · Mathematics 2025-04-14 Lucas Mieg , Martin Mönnigmann

We establish analogues of Liouville's theorem in the complex function theory, with the differential operator replaced by various difference operators. This is done generally by the extraction of (formal) Taylor coefficients using a residue…

Complex Variables · Mathematics 2022-11-03 Kam Hang Cheng , Yik-Man Chiang , Avery Ching

Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…

Signal Processing · Electrical Eng. & Systems 2025-08-06 Na Liu , Chengliang Dai , Qiuyue Wu , Qiuqi Li , Guoxiong Cai

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time…

Optimization and Control · Mathematics 2017-07-11 Hao Zhang , Clarence W. Rowley , Eric A. Deem , Louis N. Cattafesta

Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…

Systems and Control · Electrical Eng. & Systems 2024-10-07 Ningxin Liu , Shuigen Liu , Xin T. Tong , Lijian Jiang

We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…

Signal Processing · Electrical Eng. & Systems 2026-01-19 Yuki Nakamura , Shingo Takemoto , Shunsuke Ono

A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…

Fluid Dynamics · Physics 2022-09-27 Zi-Mo Liao , Zhiye Zhao , Liang-Bing Chen , Zhen-Hua Wan , Nan-Sheng Liu , Xi-Yun Lu

A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic…

Plasma Physics · Physics 2021-09-16 Indranil Nayak , Mrinal Kumar , Fernando L. Teixeira

Dynamic Mode Decomposition (DMD) is a data-driven modeling tool that generates a model from spatio-temporal data. The data needs to be as clean as possible for DMD to come up with a faithful model. We review a few data-filtering methods to…

Optimization and Control · Mathematics 2021-03-04 Moajjem H. Chowdhury , Nazmul Islam Shuzan , Mohammad N. Murshed , Sanwar Alam , M. Monir Uddin , Zarin Subah

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Machine Learning · Computer Science 2020-02-23 Patrick Heas , Cedric Herzet , Benoit Combes

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…

Machine Learning · Statistics 2026-03-27 Noah Steidle , Joppe De Jonghe , Mariya Ishteva

Structural damage detection using non-contact sensing remains a challenging problem in structural health monitoring. This study presents a data-driven framework based on Dynamic Mode Decomposition (DMD) for extracting structural dynamics…

Systems and Control · Electrical Eng. & Systems 2026-05-05 R K B M Rizmi , Shabbir Ahmed

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

Signal Processing · Electrical Eng. & Systems 2020-04-09 Mustaffa Alfatlawi , Vaibhav Srivastava

A semiclassical approximation for an evolving density operator, driven by a "closed" hamiltonian operator and "open" markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the…

Quantum Physics · Physics 2020-08-18 A. M. Ozorio de Almeida , P. de M. Rios , O. Brodier