On the Dynamic Data-Driven Simulation of Coupled Models

Dynamic Data-Driven Application Systems – DDDAS – appear as a new paradigm in the field ofapplied sciences and engineering, and in particular in simulation-based engineering sciences. ByDDDAS we mean a set of techniques that allow the linkage of simulation tools with measurementdevices for real-time control of systems and processes.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. DDDASneeds for accurate and fast simulation tools making use if possible of off-line computations forlimiting as much as possible the on-line computations.We could define efficient solvers by introducing all the sources of variability as extra-coordinates inorder to solve off-line only once the model to obtain its most general solution to be then consideredin on-line purposes. However, such models result defined in highly multidimensional spacessuffering the so-called curse of dimensionality.We proposed recently a technique, the Proper Generalized Decomposition – PGD-, able tocircumvent the redoubtable curse of dimensionality. The marriage of DDDAS concepts and tools andPGD off-line computations could open unimaginable possibilities in the field of dynamics data-driven application systems.In this work we explore some possibilities in the context of coupled models. The parametricmodeling of coupled models constitutes an opportunity for addressing on-line inverse analysis ofoptimization of usual multiphysics models. In our former works we have investigates the DDDASapplied to linear [1] or non linear [2] dynamical systems as well as to models described by linear ornon-linear partial differential equations [3]. In the present work we generalized the approach foraddressing coupled models