The design and deployment of Digital Twins (DTs) of a physical asset require seamless integration of multi-scale / multi-physics numerical models and observational data, which can have various degrees of fidelity. Despite significant advances in hardware, computing, and data analytics, complex systems of practical significance defy their robust and reliable high-fidelity, DT-like representations. The successful deployment of DT technology calls for a new developmental paradigm, requiring new mathematical and computational methods that integrate physics-based modeling with data-driven methods, operating across different spatial and temporal scales and supporting real-time decision making under uncertainty. This minisymposium brings together researchers in mathematics, computational science, and engineering to explore recent advances and open challenges in the development of mathematically grounded DTs. Topics of interest include: 1) methods for bidirectional data flow between digital and physical systems, 2) model reduction methods that preserve essential physics while enabling real-time performance, 3) operator learning of partial differential equations, 4) scalable methods for uncertainty quantification and probabilistic inference, 5) optimization and control strategies tailored for live environments, 6) hybrid methods integrating scientific machine learning with traditional simulation methods, 7) complex systems representations, 8) continual learning systems. 
By focusing on the mathematical foundations and computational methods that underpin DT technology, this MS aims to create new collaborations across disciplines and foster the development of rigorous, reliable, and scalable DTs.