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.

中文翻译：

---

模型缩减的插值方法 [书架]


人们对机器学习兴趣的激增导致人们越来越重视准确、高效的替代模型的价值。本书分为四个部分。第 1 部分由第 1 章和第 2 章组成，向读者介绍了一般模型简化的基本思想，并提供了本书其余部分所需的相关系统理论背景。第 2 部分由第 3 章到第 5 章组成，涵盖了插值模型简化​​的核心概念，其中以紧凑而深入的方式呈现了众所周知的结果和最先进的实现。第 3 部分由第 6 章和第 7 章组成，首次全面地阐述了参数相关动力系统和非线性插值模型简化​​的最新发展。这本书及时提醒我们，在我们使用黑盒逼近函数（通常需要大量数据来训练）之前，系统理论模型简化方法有着悠久而严格的历史（以及许多最新进展），可以在广泛的科学和工程环境中提供结构化的降阶模型。