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.

17 pages, 12 figures