Through increasingly available data, today's structures comprise a cyber-physical character, which fosters refinement of our approach to modelling and managing these systems. Yet, pure reliance on data is often not sufficient. Black box schemes often struggle with the intricate dynamics and uncertainties inherent to advanced modelling tasks. This talk overviews an integrative framework that advances learning for dynamics simulations, monitoring, and digital twinning tasks by focusing on the use of appropriate representations.

Central to this approach is the encoding of data into forms that effectively capture system behaviors, leveraging appropriate architectures, and hybridizing physics-based principles with machine learning. We discuss integration of structured representations and formal grammars to enable the characterization of dynamic behaviors and foster learning models that are interpretable, adaptable, and generalizable. This physics-enhanced paradigm enables efficient simulation of complex systems, whether in forward open-loop or closed-loop configurations, accommodating scenarios with or without integrated data. By exploring these representational strategies, this presentation outlines a roadmap toward resilient and self-aware systems.