  This paper presents a fast approach to simulating muons produced in
interactions of the SPS proton beams with the target of the SHiP experiment.
The SHiP experiment will be able to search for new long-lived particles
produced in a 400~GeV$/c$ SPS proton beam dump and which travel distances
between fifty metres and tens of kilometers. The SHiP detector needs to operate
under ultra-low background conditions and requires large simulated samples of
muon induced background processes. Through the use of Generative Adversarial
Networks it is possible to emulate the simulation of the interaction of
400~GeV$/c$ proton beams with the SHiP target, an otherwise computationally
intensive process. For the simulation requirements of the SHiP experiment,
generative networks are capable of approximating the full simulation of the
dense fixed target, offering a speed increase by a factor of
$\mathcal{O}(10^6)$. To evaluate the performance of such an approach,
comparisons of the distributions of reconstructed muon momenta in SHiP's
spectrometer between samples using the full simulation and samples produced
through generative models are presented. The methods discussed in this paper
can be generalised and applied to modelling any non-discrete multi-dimensional
distribution.
