A Novel Approach for Parametric Dynamic Mode Decomposition: Application to the DYNASTY Experimental Facility

Learning models from data has become quite popular recently due to the significant developments in artificial intelligence and the availability of large amounts of data. Nevertheless, this topic has already been addressed in the past by methodologies belonging to the Reduced Order Modelling framework: in particular, one of the most famous equation-free techniques is the Dynamic Mode Decomposition (DMD), an algorithm designed to learn the best linear model underlying some physical phenomena starting from the knowledge of time series datasets. Hence, this method can find the best state matrix of a dynamical system to advance in time even beyond the span of the original dataset. In its standard formulation, DMD cannot deal with parametric time series, and a different linear model must be derived for each realization of the parameter: this work proposes a novel approach to tackle this problem by treating the linear DMD operators as snapshot data, from which a reduced representation can be obtained. Then, it is only sufficient to learn the map between the parameters and the modal coefficients of the reduced expansion of the DMD operators. In this perspective, this approach stands as a generalization of linearization methods to learn a broader class of transient phenomena within the same framework. This novel methodology has been applied to a RELAP5 model of the DYNASTY experimental facility built at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation IV applications, especially in the case of Circulating Fuel reactors.