Multi‐fidelity data fusion through parameter space reduction with applications to automotive engineering

Abstract

Abstract Multi‐fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high‐dimensional scalar functions with low intrinsic dimensionality. By introducing a low dimensional bias we can fight the curse of dimensionality affecting these quantities of interest, especially for many‐query applications. We seek a gradient‐based reduction of the parameter space through linear active subspaces or a nonlinear transformation of the input space. Then we build a low‐fidelity response surface based on such reduction, thus enabling nonlinear autoregressive multi‐fidelity Gaussian process regression without the need of running new simulations with simplified physical models. This has a great potential in the data scarcity regime affecting many engineering applications. In this work we present a new multi‐fidelity approach that involves active subspaces and the nonlinear level‐set learning method, starting from the preliminary analysis previously conducted (Romor F, Tezzele M, Rozza G. Proceedings in Applied Mathematics & Mechanics . Wiley Online Library; 2021). The proposed framework is tested on two high‐dimensional benchmark functions, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces.