  Differential measurements of particle collisions or decays can provide
stringent constraints on physics beyond the Standard Model of particle physics.
In particular, the distributions of the kinematical and angular variables that
characterise heavy me- son multibody decays are non trivial and can sign the
underlying interaction physics. In the era of high luminosity opened by the
advent of the Large Hadron Collider and of Flavor Factories, differential
measurements are less and less dominated by statistical precision and require a
precise determination of efficiencies that depend simultaneously on several
variables and do not factorise in these variables. This docu- ment is a
reflection on the potential of multivariate techniques for the determination of
such multidimensional efficiencies. We carried out two case studies that show
that multilayer perceptron neural networks can determine and correct for the
distortions introduced by reconstruction and selection criteria in the
multidimensional phase space of the decays $B^{0}\rightarrow K^{*0}(\rightarrow
K^{+}\pi^{-}) \mu^{+}\mu^{-}$ and $D^{0}\rightarrow
K^{-}\pi^{+}\pi^{+}\pi^{-}$, at the price of a minimal analysis effort. We
conclude that this method can already be used for measurements which
statistical precision does not yet reach the percent level and that with more
sophisticated machine learning methods, the aforementioned potential is very
promising.
