Dynamic Data-Driven Application Systems constitute nowadays one of the most challenging applications of simulation-based Engineering Science [1]. DDDAS imply a set of techniques that allow the linkage of simulation tools with measurement devices for real-time control of systems and processes [2]. DDDAS entails the ability to dynamically incorporate additional data into an executing application, and in reverse, the ability of an application to dynamically steer the measurement process. These systems need accurate and fast simulation tools, hence the off-line computations to limit as much as possible the on-line computations. In order to obtain the most efficient solver, all the sources of variability are introduced as extra-coordinates as to solve only once the model off-line to obtain its most general solution to be then considered in on-line purpose. However, such models result defined in highly multidimensional spaces. A technique recently proposed, called Proper Generalized Decomposition [3], allows circumventing this redoubtable curse of dimensionality.

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