Physics-Based and Data-Driven Modeling for Digital Twins

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 The (Executable) Digital Twin: merging the digital and the physical worlds.- Chapter 2 Digital Twins: modeling hierarchy and basic approaches.- Chapter 3 Adaptive planning for risk-aware predictive digital twins.- Chapter 4 Recurrent deep Kernel Learning of Dynamical Systems.-Chapter 5 Hierarchical modeling for an industrial implementation of a digital twin for electrical drives.-Chapter 6 Deviation-sensitive black-box anomaly attribution.

Karim Cherifi is a researcher at the University of Wuppertal, Germany. His main research interests include model order reduction, data-driven modeling, Port Hamiltonian modeling, and modeling for digital twins. He obtained his Ph.D. in Control theory in 2019 from the Institute of Electrical and Electronic Engineering in Boumerdes (Algeria). Afterward, he was a postdoctoral researcher at the Max Planck Institute (MPI) for Dynamics of Complex Technical Systems in Magdeburg (Germany)and later at the Technical University of Berlin (Germany) where he was involved in the design of digital twins for Large Drive Applications within the project ’Elektrische Antriebe 2.0’ as part of the Werner-von-Siemens Centre for Industry and Science in Berlin. Recently, he has been involved in multiple projects that implement digital twins in different domains: electrical machines, Building information modeling (BIM), and gas networks.  

Bio Ion Victor Gosea is a senior scientist at the Max Planck Institute (MPI) for Dynamics of Complex Technical Systems in Magdeburg, Germany, in the Computational Methods in Systems and Control Theory Group led by Prof. Peter Benner. His main research interests include data-driven model reduction and reduced-order modeling of dynamical systems, system identification, rational approximation, and surrogate modeling for efficient and predictive digital twins. He obtained a Ph.D. in Electrical Engineering in 2017 at the Jacobs University Bremen, Germany. Afterward, he was a postdoctoral researcher at the MPI Magdeburg, specializing in frequency-domain data-driven methods. In the last years, he has been part of research endeavors and projects that aim at constructing digital twins for process, chemical, and electrochemical engineering applications, with an emphasis on developing green carbon processes in the context of the Power-to-X conversion framework.