  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.
