  In this work we introduce RAPIDD, a surrogate model that speeds up the
computation of the expected spectrum of dark matter particles in direct
detection experiments. RAPIDD replaces the exact calculation of the dark matter
differential rate (which in general involves up to three nested integrals) with
a much faster parametrization in terms of ordinary polynomials of the dark
matter mass and couplings, obtained in an initial training phase. In this
article, we validate our surrogate model on the multi-dimensional parameter
space resulting from the effective field theory description of dark matter
interactions with nuclei, including also astrophysical uncertainties in the
description of the dark matter halo. As a concrete example, we use this tool to
study the complementarity of different targets to discriminate simplified dark
matter models. We demonstrate that RAPIDD is fast and accurate, and
particularly well-suited to explore a multi-dimensional parameter space, such
as the one in effective field theory approach, and scans with a large number of
evaluations.
