Interpolatory Methods for Model Reduction [Bookshelf

Abstract

The surge of interest in machine learning has led to increased emphasis on the value of accurate, efficient surrogate models. The book is divided into four parts. Part 1, consisting of Chapters 1 and 2, introduces the reader to the basic ideas underlying general model reduction and provides the relevant system-theoretic background needed for the remainder of the book. Part 2, consisting of Chapters 3–5, covers core concepts of interpolatory model reduction where wellknown results and state-of-the-art implementations are presented in a compact yet deep way. Part 3, consisting of Chapters 6 and 7, provides the first comprehensive textbook exposition of recent developments in parameter dependent dynamical systems and nonlinear interpolatory model reduction. This book is a timely reminder that before we reach for black-box approximation functions (which often require prohibitive amounts of data to train), there is a long and rigorous history (and many recent advances) in system-theoretic model-reduction methods that can deliver structured, reduced-order models in a broad range of scientific and engineering settings.