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A digital twin (DT) is a computational model that evolves over time to persistently represent the structure, behavior, and context of a unique physical system or process. DTs are characterized by a dynamic and continuous two-way flow of information between the computational model and the physical system. Data streams from the physical system are assimilated into the computational model to reduce uncertainties and improve predictions of the model, which in turn is used as a basis for controlling the physical system, optimizing data acquisition, and providing decision support. The DT must execute rapidly enough to support decisions and controls in time scales relevant to the physical system, and must manage and quantify uncertainties across its lifecycle. Interest in the DT paradigm is growing rapidly across a range of application areas as a way to construct, manage, and capitalize on state-of-the-art computational models, data-driven learning, and decision making under uncertainty for many complex engineered and natural systems. Indeed, the global market for DTs in industry alone is projected to grow to $156 billion by 2030.
This workshop will focus on mathematical, statistical, and computational foundations underlying DTs, in particular addressing challenges in (1) data assimilation and statistical inverse problems, (2) optimal control and decision making, (3) optimal experimental design, and (4) model reduction and surrogates, all in the context of DTs of complex systems. While these fields are “classical,” fundamental challenges arise in the DT setting due to the tight, dynamic interplay between assimilation and control/decisions, the rapid time scales needed for response, the need for predictivity of reduced models/surrogates over control and parameter spaces, and the need for robustness to data and model uncertainties to support high-consequence decisions. These present frontier mathematical, statistical, and computational challenges. The workshop will feature talks and discussion on the four foundational areas identified above, and on the integration of these to address complex applications of DTs to scientific, engineering, medical, and societal problems.