  In this work, we develop a simulation-based model to predict the density
split (DSS) and second-order shear and clustering statistics. A
simulation-based model has the potential to model highly non-linear scales
where current DSS models fail. To build this model, we use the
\texttt{AbacusSummit} N-body simulation suite from which we measure all
necessary statistics and train an emulator based on \texttt{CosmoPower}. In
that context, we discuss possible improvements for future emulators to make the
measurement less noisy and biased, resulting in more accurate and precise model
predictions.
  Regarding the emulator's accuracy, we find that the most important aspect is
the average of the summary statistics over multiple-shot noise realizations of
the foreground galaxies. However, these results probably depend on the chosen
number density of the foreground galaxies. Regarding the parameter forecast
based on preliminary LOWZxUNIONS data, we find that DSS has more constraining
power to derive cosmological parameters and that the joint analysis with
second-order statistics is particularly useful for extracting parameters of the
galaxy-halo connection.
