  Multi-fidelity approaches combine different models built on a scarce but
accurate data-set (high-fidelity data-set), and a large but approximate one
(low-fidelity data-set) in order to improve the prediction accuracy. Gaussian
Processes (GPs) are one of the popular approaches to exhibit the correlations
between these different fidelity levels. Deep Gaussian Processes (DGPs) that
are functional compositions of GPs have also been adapted to multi-fidelity
using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model
increases the expressive power compared to GPs by considering non-linear
correlations between fidelities within a Bayesian framework. However, these
multi-fidelity methods consider only the case where the inputs of the different
fidelity models are defined over the same domain of definition (e.g., same
variables, same dimensions). However, due to simplification in the modeling of
the low-fidelity, some variables may be omitted or a different parametrization
may be used compared to the high-fidelity model. In this paper, Deep Gaussian
Processes for multi-fidelity (MF-DGP) are extended to the case where a
different parametrization is used for each fidelity. The performance of the
proposed multifidelity modeling technique is assessed on analytical test cases
and on structural and aerodynamic real physical problems.
