  The Gaussian Process (GP)-based surrogate model has the inherent capability
of capturing the anomaly arising from limited data, lack of data, missing data,
and data inconsistencies (noisy/erroneous data) present in the modeling and
simulation component of the digital twin framework, specifically for the
accident tolerant fuel (ATF) concepts. However, GP will not be very accurate
when we have limited high-fidelity (experimental) data. In addition, it is
challenging to apply higher dimensional functions (>20-dimensional function) to
approximate predictions with the GP. Furthermore, noisy data or data containing
erroneous observations and outliers are major challenges for advanced ATF
concepts. Also, the governing differential equation is empirical for
longer-term ATF candidates, and data availability is an issue. Physics-informed
multi-fidelity Kriging (MFK) can be useful for identifying and predicting the
required material properties. MFK is particularly useful with low-fidelity
physics (approximating physics) and limited high-fidelity data - which is the
case for ATF candidates since there is limited data availability. This chapter
explores the method and presents its application to experimental thermal
conductivity measurement data for ATF. The MFK method showed its significance
for a small number of data that could not be modeled by the conventional
Kriging method. Mathematical models constructed with this method can be easily
connected to later-stage analysis such as uncertainty quantification and
sensitivity analysis and are expected to be applied to fundamental research and
a wide range of product development fields. The overarching objective of this
chapter is to show the capability of MFK surrogates that can be embedded in a
digital twin system for ATF.
