A Gentle Introduction to Data, Learning, and Model Order Reduction

This open access book explores the latest advancements in simulation performance, driven by model order reduction, informed and augmented machine learning technologies and their combination into the so-called hybrid digital twins. It provides a comprehensive review of three key frameworks shaping modern engineering simulations: physics-based models, data-driven approaches, and hybrid techniques that integrate both. The book examines the limitations of traditional models, the role of data acquisition in uncovering underlying patterns, and how physics-informed and augmented learning techniques contribute to the development of digital twins. Organized into four sections— Around Data, Around Learning, Around Reduction, and Around Data Assimilation & Twinning —this book offers an essential resource for researchers, engineers, and students seeking to understand and apply cutting-edge simulation methodologies