In recent years, algorithms aiming at learning 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 dataset: its output is a best state operator of the underlying dynamical system that can be used, in principle, to advance the original dataset in time even beyond its span. 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 parameter realization. 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-hydraulics problems are considered: two benchmark 'flow over cylinder' test cases at diverse Reynolds numbers, whose datasets are, respectively, obtained with the FEniCS finite element solver and retrieved from the CFDbench dataset, 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, whose dataset was generated using the RELAP5 nodal solver.

翻译：近年来，从可用数据中学习模型的算法因两大因素而广受欢迎：1）人工智能技术的显著发展；2）海量数据的可获得性。然而，该课题早已通过降阶建模框架下的方法论得到处理，其中最具代表性的无方程技术当属动态模态分解。该算法旨在学习能够表征时间序列数据集所描述物理现象的最佳线性模型：其输出是底层动力系统的最佳状态算子，原则上可用于将原始数据集在时间维度上推进，甚至超越其原有时间跨度。然而，在该技术的标准表述中，无法处理参数化时间序列，这意味着需要为每个参数实现推导不同的线性模型。相关研究正在进行中，目前已存在若干参数化动态模态分解的变体。本研究通过比较当前部署的不同算法，并评估其相互间的优势与不足，为该研究领域作出贡献。为此，我们考虑了三个不同的热工水力问题：两个不同雷诺数下的"圆柱绕流"基准测试案例（其数据集分别通过FEniCS有限元求解器获得和从CFDbench数据集中提取），以及米兰理工大学运行的DYNASTY实验装置（该装置研究第四代核能应用中由内部加热流体建立的自然循环现象，其数据集使用RELAP5节点求解器生成）。