Modeling Nonlinear Dynamics from Equations and Data with Applications to Solids, Fluids, and Controls (Hardcover)

George Haller

ISBN 10: 1611978343 / ISBN 13: 9781611978346

Published by Society for Industrial & Applied Mathematics,U.S., New York, 2025

About this Item

Hardcover. This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control. AudienceThis book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling. An innovative method reduces complex nonlinear equations to spectral submanifolds (SSMs), low-dimensional invariant structures that capture the essence of system dynamics with precision. Applications in fluid and solid mechanics and control theory demonstrate the power of these mathematically sound, predictive models. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9781611978346

Bibliographic Details

• Title: Modeling Nonlinear Dynamics from Equations and Data with Applications to Solids, Fluids, and Controls (Hardcover)
• Publisher: Society for Industrial & Applied Mathematics,U.S., New York
• Publication Date: 2025
• Language: English
• ISBN 10: 1611978343
• ISBN 13: 9781611978346
• Binding: Hardcover
• Condition: new

About this title

Synopsis

“George Haller provides a substantial literature overview which, in combination with his many contributions, results in the first book on spectral model reduction techniques. He covers basic theory for both linear and nonlinear problems and model- and data-driven techniques, and he demonstrates the method’s excellent behavior on nontrivial problems.” – Jan S. Hesthaven, Karlsruhe Institute of Technology (KIT) “This is an exciting topic and a powerful method that already has and will continue to have an impact on any field where model reduction is a key ingredient or a central concern. The content is presented in a logical order, from the equation-based to the data-driven version of the method to applications that progressively increase in complexity.” – Peter Schmid, KAUST This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control.

About the Author

George Haller is a professor of mechanical engineering at ETH Zürich, where he holds the Chair in Nonlinear Dynamics and heads the Institute for Mechanical Systems. His prior appointments include tenured faculty positions at Brown, McGill, and MIT. He also served as the inaugural director of Morgan Stanley’s fixed-income modeling center. Professor Haller is the recipient of a Sloan Fellowship in mathematics, an ASME Thomas Hughes Young Investigator Award, a School of Engineering Distinguished Professorship (McGill), the Stanley Corrsin Award of the APS, and the Lyapunov Award of the ASME. He is an external member of the Hungarian Academy of Science and a fellow of SIAM, APS, and ASME.