  One of the important goals of the proposed future $e^+e^-$ collider
experiments is the search for dark matter particles using different
experimental approaches. The most general search approach is based on the
mono-photon signature, which is expected when production of the invisible final
state is accompanied by a hard photon from initial state radiation. Analysis of
the energy spectrum and angular distributions of those photons can shed light
on the nature of dark matter and its interactions. Therefore, it is crucial to
be able to simulate the signal and background samples in a uniform framework,
to avoid possible systematic biases. The WHIZARD program is a flexible tool,
which is widely used by $e^+e^-$ collaborations for simulation of many
different "new physics" scenarios. We propose the procedure of merging the
matrix element calculations with the lepton ISR structure function implemented
in WHIZARD. It allows us to reliably simulate the mono-photon events, including
the two main Standard Model background processes: radiative neutrino pair
production and radiative Bhabha scattering. We demonstrate that cross sections
and kinematic distributions of mono-photon in neutrino pair-production events
agree with corresponding predictions of the KKMC, a Monte Carlo generator
providing perturbative predictions for SM and QED processes, which has been
widely used in the analysis of LEP data.
