Dynamic Data-Driven Parametric Dynamical Systems

International audienceDynamic Data-Driven Application Systems – DDDAS – appear as a new paradigm in the field of applied sciences and engineering, and in particular in simulation-based engineering sciences. By DDDAS we mean a set of techniques that allow the linkage of simulation tools with measurement devices 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. DDDAS needs for accurate and fast simulation tools making use if possible of off-line computations for limiting as much as possible the on-line computations. We could define efficient solvers by introducing all the sources of variability as extra-coordinates in order to solve the model off-line only once to obtain its most general solution to be then considered in on-line purposes. In this work we are evaluating one such strategy in both linear and non-linear dynamical systems as the ones usually encountered in control, epidemiology models, physiological systems (diagnostic of diabetes …). Such models result defined in highly multidimensional spaces suffering the so-called curse of dimensionality that could be efficiently circumvented by applying a Proper Generalized Decomposition that constitutes a work in progress