Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities

TL;DR

This paper reviews Gaussian process-based multi-fidelity modeling techniques that handle variable relationships between models, comparing their performance on analytical and aerospace engineering problems to guide effective model fusion.

Contribution

It provides a unified overview of Gaussian process multi-fidelity methods accommodating different fidelity relationships, with numerical comparisons on diverse test cases.

Findings

Techniques vary in effectiveness depending on fidelity relationship complexity.

Unified framework highlights connections between different Gaussian process approaches.

Performance assessment guides selection of methods based on problem characteristics.

Abstract

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.