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Explore the intersection of Structural Health Monitoring (SHM) and digital twin technology in this hour-long lecture on twinning and model discovery for engineered systems. Delve into the complexities of modern engineering structures and their operation under varying loads and adverse environments. Learn about the hierarchy of SHM, from damage detection to performance prognosis, and understand why purely data-driven methods fall short for higher-level tasks. Discover how integrating physics-based representations with data-driven approaches can create robust monitoring systems for engineered structures. Examine the concept of augmented twin representations and their potential for anticipating performance and advising on preventive actions. Gain insights from Associate Professor Eleni Chatzi, an expert in structural mechanics and monitoring, as she shares her research on intelligent data-driven assessment for engineered systems.