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Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate…

Fluid Dynamics · Physics 2016-03-23 Scott T. M. Dawson , Maziar S. Hemati , Matthew O. Williams , Clarence W. Rowley

We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…

Machine Learning · Computer Science 2025-02-14 Yunpeng Zhu , Liangliang Cheng , Anping Jing , Hanyu Huo , Ziqiang Lang , Bo Zhang , J. Nathan Kutz

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

Numerical Analysis · Mathematics 2023-01-25 Quincy A. Huhn , Mauricio E. Tano , Jean C. Ragusa , Youngsoo Choi

Molecular dynamics (MD) simulation is a powerful computational tool to study the behavior of macromolecular systems. But many simulations of this field are limited in spatial or temporal scale by the available computational resource. In…

Computational Physics · Physics 2010-01-22 Ji Xu , Ying Ren , Wei Ge , Xiang Yu , Xiaozhen Yang , Jinghai Li

This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…

Dynamical Systems · Mathematics 2013-12-19 Steven L. Brunton , Joshua L. Proctor , J. Nathan Kutz

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue…

Numerical Analysis · Computer Science 2011-11-28 Vedran Novakovic , Sanja Singer

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…

Computational Physics · Physics 2018-02-27 Yilang Liu , Weiwei Zhang , Jiaqing Kou

Dynamic mode decomposition (DMD) is a powerful and increasingly popular tool for performing spectral analysis of fluid flows. However, it requires data that satisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments,…

Fluid Dynamics · Physics 2014-09-17 Jonathan H. Tu , Clarence W. Rowley , J. Nathan Kutz , Jessica K. Shang

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Numerical Analysis · Mathematics 2024-01-17 Francesco Andreuzzi , Nicola Demo , Gianluigi Rozza

Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…

Numerical Analysis · Mathematics 2022-02-15 Tim Krake , Daniel Weiskopf , Bernhard Eberhardt

The traditional method of computing singular value decomposition (SVD) of a data matrix is based on a least squares principle, thus, is very sensitive to the presence of outliers. Hence the resulting inferences across different applications…

Statistics Theory · Mathematics 2024-09-17 Subhrajyoty Roy , Abhik Ghosh , Ayanendranath Basu

We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…

Data Structures and Algorithms · Computer Science 2025-01-20 Artur Czumaj , Gopinath Mishra , Anish Mukherjee

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Optimization and Control · Mathematics 2014-09-24 Joshua L. Proctor , Steven L. Brunton , J. Nathan Kutz

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

We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and…

Mathematical Software · Computer Science 2018-08-15 Aaron Montag , Jürgen Richter-Gebert

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…

Machine Learning · Computer Science 2024-03-13 Łukasz Struski , Paweł Morkisz , Przemysław Spurek , Samuel Rodriguez Bernabeu , Tomasz Trzciński

Large video diffusion and flow models have achieved remarkable success in high-quality video generation, but their use in real-time interactive applications remains limited due to their inefficient multi-step sampling process. In this work,…

Computer Vision and Pattern Recognition · Computer Science 2026-01-16 Weili Nie , Julius Berner , Nanye Ma , Chao Liu , Saining Xie , Arash Vahdat

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Systems and Control · Computer Science 2019-06-26 Daniel Dylewsky , Molei Tao , J. Nathan Kutz

Dynamic programming (DP) is a cornerstone of combinatorial optimization, yet its inherently sequential structure has long limited its scalability in scenario-based stochastic programming (SP). This paper introduces a GPU-accelerated…

Optimization and Control · Mathematics 2025-11-25 Jingyi Zhao , Linxin Yang , Haohua Zhang , Tian Ding

Distillation-based acceleration has become foundational for making autoregressive streaming video diffusion models practical, with distribution matching distillation (DMD) as the de facto choice. Existing methods, however, train the student…

Computer Vision and Pattern Recognition · Computer Science 2026-05-06 Bin Wu , Mengqi Huang , Shaojin Wu , Weinan Jia , Yuxin Wang , Zhendong Mao , Yongdong Zhang