A Digital Twin (DT) is a representation of a real-world system that continuously exchanges data between digital models and their physical counterparts, allowing them to simulate, monitor, and predict the behavior of real-world systems in real-time. As such, DTs hold transformative potential across critical sectors including manufacturing, infrastructure, energy, and defense. However, existing methods for updating the digital models with real-world data are often too slow for real-time use. To overcome this barrier, this research introduces a novel mathematical and computational framework to dramatically accelerate digital model calibration, enabling faster and more accurate digital twin applications. The potential benefits of this work are far-reaching, advancing capabilities in predictive maintenance, process optimization, and risk mitigation, directly supporting the US economic productivity, public safety, technological innovation, and competitiveness. The project also fosters the next generation of scientists and engineers through interdisciplinary training and hands-on research experiences for graduate and undergraduate students. Together, these contributions lay the groundwork for a new generation of scalable, real-time Digital Twin systems with wide-reaching impact across science, industry, and education. Digital Twins require continuous two-way communication between physical systems and high-fidelity digital models. However, the cost in time and resources to update