Cope with diverse data structures in multi-fidelity modeling: A Gaussian process method

Multi-fidelity modeling (MFM) frameworks, especially the Bayesian MFM, have gained popularity in simulation based modeling, uncertainty quantification and optimization, due to the potential for reducing computational budget. In the view of multi-output modeling, the MFM approximates the high-/low-fidelity outputs simultaneously by considering the output correlations, and particularly, it transfers knowledge from the inexpensive low-fidelity outputs that have many training points to enhance the modeling of the expensive high-fidelity output that has a few training points. This article presents a novel multi-fidelity Gaussian process for modeling with diverse data structures. The diverse data structures mainly refer to the diversity of high-fidelity sample distributions, i.e., the high-fidelity points may randomly fill the domain, or more challengingly, they may cluster in some subregions. The proposed multi-fidelity model is composed of a global trend term and a local residual term. Particularly, the flexible residual term extracts both the shared and output-specific residual information via a data-driven weight parameter. Numerical experiments on two synthetic examples, an aircraft example and a stochastic incompressible flow example reveal that this very promising Bayesian MFM approach is capable of effectively extracting the low-fidelity information for facilitating the modeling of the high-fidelity output using diverse data structures.