Model Reduction Of Complex Dynamical Systems

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Model Reduction Of Complex Dynamical Systems

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Author : Peter Benner
language : en
Publisher:
Release Date : 2021

Model Reduction Of Complex Dynamical Systems written by Peter Benner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems - MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

Model Reduction Of Complex Dynamical Systems

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Author : Peter Benner
language : en
Publisher: Springer Nature
Release Date : 2021-08-26

Model Reduction Of Complex Dynamical Systems written by Peter Benner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-26 with Mathematics categories.

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

Realization And Model Reduction Of Dynamical Systems

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Author : Christopher Beattie
language : en
Publisher: Springer Nature
Release Date : 2022-06-09

Realization And Model Reduction Of Dynamical Systems written by Christopher Beattie and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Science categories.

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.

Dimension Reduction Of Large Scale Systems

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Author : Peter Benner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Dimension Reduction Of Large Scale Systems written by Peter Benner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Technology & Engineering categories.

In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Stochastic Methods For Modeling And Predicting Complex Dynamical Systems

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Author : Nan Chen
language : en
Publisher: Springer Nature
Release Date : 2023-03-13

Stochastic Methods For Modeling And Predicting Complex Dynamical Systems written by Nan Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Mathematics categories.

This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.

Analysis And Control Of Complex Dynamical Systems

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Author : Kazuyuki Aihara
language : en
Publisher: Springer
Release Date : 2015-03-20

Analysis And Control Of Complex Dynamical Systems written by Kazuyuki Aihara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-20 with Technology & Engineering categories.

This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.

Nonlinear Model Reduction By Moment Matching

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Author : Giordano Scarciotti
language : en
Publisher:
Release Date : 2017

Nonlinear Model Reduction By Moment Matching written by Giordano Scarciotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Electronic books categories.

Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining "simpler" models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach. This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for "discontinuous" input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.

Interpolatory Methods For Model Reduction

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Author : A. C. Antoulas
language : en
Publisher: SIAM
Release Date : 2020-01-13

Interpolatory Methods For Model Reduction written by A. C. Antoulas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-13 with Mathematics categories.

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Approximation Of Large Scale Dynamical Systems

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Author : Athanasios C. Antoulas
language : en
Publisher: SIAM
Release Date : 2009-06-25

Approximation Of Large Scale Dynamical Systems written by Athanasios C. Antoulas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-25 with Mathematics categories.

Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.

34th European Symposium On Computer Aided Process Engineering 15th International Symposium On Process Systems Engineering

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Author : Flavio Manenti
language : en
Publisher: Elsevier
Release Date : 2024-06-27

34th European Symposium On Computer Aided Process Engineering 15th International Symposium On Process Systems Engineering written by Flavio Manenti and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-27 with Technology & Engineering categories.

The 34th European Symposium on Computer Aided Process Engineering / 15th International Symposium on Process Systems Engineering, contains the papers presented at the 34th European Symposium on Computer Aided Process Engineering / 15th International Symposium on Process Systems Engineering joint event. It is a valuable resource for chemical engineers, chemical process engineers, researchers in industry and academia, students, and consultants for chemical industries. - Presents findings and discussions from the 34th European Symposium on Computer Aided Process Engineering / 15th International Symposium on Process Systems Engineering joint event