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We present an estimator-based control design procedure for flow control, using reduced-order models of the governing equations, linearized about a possibly unstable steady state. The reduced models are obtained using an approximate balanced…

Optimization and Control · Mathematics 2015-05-13 Sunil Ahuja , Clarence W. Rowley

We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…

Pattern Formation and Solitons · Physics 2025-08-12 Alessandro Alla , Rudy Geelen , Hannah Lu

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

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

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…

Plasma Physics · Physics 2020-03-04 Alan A. Kaptanoglu , Kyle D. Morgan , Chris J. Hansen , Steven L. Brunton

We present a data-driven nonintrusive model order reduction method for dynamical systems with moving boundaries. The proposed method draws on the proper orthogonal decomposition, Gaussian process regression, and moving least squares…

Computational Engineering, Finance, and Science · Computer Science 2021-03-18 Zhan Ma , Wenxiao Pan

This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…

Fluid Dynamics · Physics 2025-04-09 Xukun Wang , Yilang Liu , Xiang Yang , Weiwei Zhang

A non-intrusive model order reduction (MOR) method that combines features of the dynamic mode decomposition (DMD) and the radial basis function (RBF) network is proposed to predict the dynamics of parametric nonlinear systems. In many…

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Fluid Dynamics · Physics 2021-09-22 Victor Zucatti , William Wolf

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby…

Systems and Control · Electrical Eng. & Systems 2025-04-29 Joshua Ott , Mykel J. Kochenderfer , Stephen Boyd

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust…

Fluid Dynamics · Physics 2023-08-24 Lucas F. de Souza , Renato F. Miotto , William R. Wolf

A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…

Dynamical Systems · Mathematics 2021-05-28 Matteo Diez , Andea Serani , Emilio F. Campana , Frederick Stern

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

We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of…

Fluid Dynamics · Physics 2025-07-09 Igor A. Maia , André V. G. Cavalieri

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Numerical Analysis · Mathematics 2017-04-11 Travis Askham , J. Nathan Kutz

This work aims to estimate time-resolved velocity field that is directly associated with pressure fluctuations in a subsonic round jet. To achieve this goal, synchronous measurements of the velocity field and in-flow pressure fluctuations…

Fluid Dynamics · Physics 2021-06-15 Songqi Li , Lawrence Ukeiley

Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…

Machine Learning · Computer Science 2025-08-18 Nicole Aretz , Karen Willcox

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

This paper offers a data-driven approach for designing adaptive suboptimal second-order sliding mode (ASSOSM) controllers for single-input nonlinear systems, characterized by perturbed strict-feedback structures with unknown dynamics. The…

Systems and Control · Electrical Eng. & Systems 2025-08-05 Behrad Samari , Gian Paolo Incremona , Antonella Ferrara , Abolfazl Lavaei