  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 in Romor et al. 2020. 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.
