  Data analysis of gravitational waves detected by the Ligo-Virgo-Kagra
collaboration and future observatories relies on precise modelling of the
sources. In order to build, calibrate and validate current models, we resort to
expensive simulations in Numerical Relativity (NR), the fully-fledged
simulation of Einstein's Equations. Since simulation costs and the
dimensionality of parameter space are prohibitive to perform a dense coverage,
approximate models interpolate among the available simulation data. We put
forward the technique of Gaussian Process Active Learning (GPAL), an adaptive,
data-driven protocol, for parameter space exploration and training of
gravitational wave approximants. We evaluate this proposal by studying a
computationally inexpensive scenario, in which we calibrate the approximant
TEOBResumS using the NR-informed model as a proxy for NR. In this case study,
we find that GPAL reduces the computational cost of training by a factor of 4
with respect to uniform or randomly distributed simulations. Moreover, we
consider a parallel implementation which reduces computational time, and hybrid
strategies which improve pre-calibrated models. The Gaussian Process regression
employed in this approach naturally endows the algorithm with notion of model
uncertainty. We comment on the implications of this feature for data analysis.
