Advances in Model Order Reduction: Linear and Non-Linear Perspectives – Hardcover

This book presents lectures from the Inria-CEA-EDF Summer School on Numerical Analysis, held in Paris, France, from 1 to 5 July 2024. It provides an in-depth introduction to recent advances in intrusive and non-intrusive, physics-based model order reduction (MOR), with particular emphasis on nonlinear approximation techniques. The lectures cover:

• Fundamentals of projection-based MOR for parametric systems, including an overview of Galerkin and Petrov-Galerkin projection methods, an introduction to hyperreduction based on empirical quadrature, and a discussion of quadratic and neural-network-augmented nonlinear approximations;
• Nonlinear approximations via coordinate transformations, including applications of optimal transport and registration methods to nonlinear problems;
• Localized methods, including the combination of domain decomposition methods with model reduction techniques for ROM-FOM coupling and the treatment of multiphysics problems through localized training and model reduction;
• Subspace interpolation and dynamic mode decomposition, including techniques for handling unsteady problems through subspace interpolation and dynamic mode decomposition (DMD);
• Tutorials and hands-on exercises with accompanying Python code and notebooks that support the practical implementation of the methods presented.

The book combines mathematical foundations, recent methodological developments, and computational practice, making it a valuable resource for graduate students, researchers, and practitioners working in numerical analysis, scientific computing, computational engineering, and data-driven modeling.