Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes

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