  The design process of complex systems such as new configurations of aircraft
or launch vehicles is usually decomposed in different phases which are
characterized for instance by the depth of the analyses in terms of number of
design variables and fidelity of the physical models. At each phase, the
designers have to compose with accurate but computationally intensive models as
well as cheap but inaccurate models. Multi-fidelity modeling is a way to merge
different fidelity models to provide engineers with accurate results with a
limited computational cost. Within the context of multi-fidelity modeling,
approaches relying on Gaussian Processes emerge as popular techniques to fuse
information between the different fidelity models. The relationship between the
fidelity models is a key aspect in multi-fidelity modeling. This paper provides
an overview of Gaussian process-based multi-fidelity modeling techniques for
variable relationship between the fidelity models (e.g., linearity,
non-linearity, variable correlation). Each technique is described within a
unified framework and the links between the different techniques are
highlighted. All the approaches are numerically compared on a series of
analytical test cases and four aerospace related engineering problems in order
to assess their benefits and disadvantages with respect to the problem
characteristics.
