In recent years, algorithms aiming to learn models from available data have become quite popular due to two factors: (1) the significant developments in artificial intelligence techniques and (2) the availability of large amounts of data. Nevertheless, this topic has already been addressed by methodologies belonging to the reduced order modelling framework, of which perhaps the most famous equation-free technique is dynamic mode decomposition. This algorithm aims to learn the best linear model that represents the physical phenomena described by a time series data set. Its output is a best-fit linear operator of the underlying dynamical system that can be used, in principle, to advance the system itself in time even beyond the training time interval. However, in its standard formulation, this technique cannot deal with parametric time series, meaning that a different linear model has to be derived for each configuration. Research on this is ongoing, and some versions of a parametric dynamic mode decomposition already exist.

This work contributes to this research field by comparing the different algorithms presently deployed and assessing their advantages and shortcomings compared to each other. To this aim, three different thermal-hydraulic problems are considered: two benchmark flow-over cylinder test cases at diverse Reynolds numbers, and the DYNASTY experimental facility operating at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation-IV nuclear applications simulated using the RELAP5 nodal solver. As a key result, this paper highlights the main advantages and disadvantages of the available parametric dynamic mode decomposition methods, concluding that the choice of the algorithm version strongly depends on the problem under consideration and on the user’s priority (i.e. accuracy or computational speed of the online phase). Additionally, this paper shows that an interpretable linear model can be learned from parametric data sets governed by nonlinear models that can be used for parameter interpolation, and most importantly, for state prediction in time.