  Gaussian processes are employed for non-parametric regression in a Bayesian
setting. They generalize linear regression, embedding the inputs in a latent
manifold inside an infinite-dimensional reproducing kernel Hilbert space. We
can augment the inputs with the observations of low-fidelity models in order to
learn a more expressive latent manifold and thus increment the model's
accuracy. This can be realized recursively with a chain of Gaussian processes
with incrementally higher fidelity. We would like to extend these
multi-fidelity model realizations to case studies affected by a
high-dimensional input space but with low intrinsic dimensionality. In this
cases physical supported or purely numerical low-order models are still
affected by the curse of dimensionality when queried for responses. When the
model's gradient information is provided, the presence of an active subspace
can be exploited to design low-fidelity response surfaces and thus enable
Gaussian process multi-fidelity regression, without the need to perform new
simulations. This is particularly useful in the case of data scarcity. In this
work we present a multi-fidelity approach involving active subspaces and we
test it on two different high-dimensional benchmarks.
