Risk-Aware Digital Twins for Biomedical and Engineering System: A PDE-Constrained Optimization Perspective

Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.