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This book presents a compelling and up-to-date exploration of modeling techniques for digital twins, a transformative concept revolutionizing how physical assets are designed, operated, optimized, and managed throughout their lifecycle. Digital twins are precise virtual counterparts of physical systems, capable of integrating real-time data to offer dynamic, predictive insights into system behavior. As this paradigm gains momentum across industries, it enhances decision-making and operational efficiency but also introduces new mathematical and engineering challenges in model development.

At the core of this volume is a thorough investigation into the modeling frameworks essential for building effective digital twins. These systems must fulfill multifunctional roles, requiring models that are both robust and flexible enough to simulate complex physical processes with high fidelity. The book spans a wide spectrum of approaches from physics-based models grounded in the laws of nature to data-driven techniques that harness large-scale datasets. It also highlights the growing importance of hybrid methods that combine the interpretability of physical models with the adaptability of machine learning. Throughout the book, real-world case studies illustrate how these modeling advancements are applied to solve pressing challenges in sectors such as manufacturing, energy and transportation.

This volume brings together contributions from leading researchers who are shaping the future of digital twins. The chapters are designed to be accessible to a broad audience. Whether you just started or want to deepen your expertise, this volume offers the insights and tools needed to engage with one of the most exciting developments in modern applied mathematics and engineering. Chapter 1 is available open access under licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License in link.springer.com.