Nowadays, interest in combining mathematical knowledge about phenomena and data from the physical system is growing. Past research was devoted to developing so-called high-fidelity models, intending to make them able to catch most of the physical phenomena occurring in the system. Nevertheless, models will always be affected by uncertainties related, for example, to the parameters and inevitably limited by the underlying simplifying hypotheses on, for example, geometry and mathematical equations; thus, in a way, there exists an upper threshold of model performance. Now, research in many engineering sectors also focuses on the so-called data-driven modelling, which aims at extracting information from available data to combine it with the mathematical model. Focusing on the nuclear field, interest in this approach is also related to the Multi-Physics modelling of nuclear reactors. Due to the multiple physics involved and their mutual and complex interactions, developing accurate and stable models both from the physical and numerical point of view remains a challenging task despite the advancements in computational hardware and software, and combining the available mathematical model with data can further improve the performance and the accuracy of the former. This work investigates this aspect by applying two Data-Driven Reduced Order Modelling (DDROM) techniques, the Generalised Empirical Interpolation Method and the Parametrised-Background Data-Weak formulation, to literature benchmark nuclear case studies. The main goal of this work is to assess the possibility of using data to perform model bias correction, that is, verifying the reliability of DDROM approaches in improving the model performance and accuracy through the information provided by the data. The obtained numerical results are promising, foreseeing further investigation of the DDROM approach to nuclear industrial cases.

翻译：当前，将物理现象的数学知识与系统实测数据相结合的研究日益受到关注。以往研究致力于开发所谓的高保真模型，以期捕捉系统中发生的大部分物理现象。然而，模型始终会受到参数等不确定性因素的影响，并不可避免地受限于底层简化假设（例如几何结构或数学方程）。因此，模型性能存在固有上限。当前，众多工程领域的研究开始聚焦于数据驱动建模——通过从现有数据中提取信息，与数学模型进行融合。在核能领域，这种方法的吸引力与核反应堆的多物理场建模密切相关。由于涉及多种物理过程及其相互间复杂的耦合效应，尽管计算硬件与软件已取得显著进步，但从物理与数值角度构建精确稳定的模型仍具有挑战性，而将现有数学模型与数据相结合可进一步提升模型性能与精度。本研究通过应用广义经验插值法和参数化背景数据弱形式两种数据驱动降阶建模技术，对文献中核能基准案例进行了探索性分析。核心目标在于评估利用数据进行模型偏差修正的可行性，即验证DDROM方法能否借助数据信息改善模型性能与精度。数值结果展现出良好前景，预示着后续可将DDROM方法拓展至核工业实际案例研究。