Machine learning (ML) is used to build a bulk microphysical parameterization including ice processes. Simulations of the Lagrangian super-particle model McSnow are used as training data. The machine learning performs a coarse-graining of the particle-resolved microphysics to multi-category two-moment bulk equations. Besides mass and number, prognostic particle properties (P3) like melt water, rime mass, and rime volume are predicted by the ML-based bulk model. The ML-based scheme is tested with simulations of increasing complexity. As a box model, the ML-based bulk scheme can reproduce the simulations of McSnow quite accurately. In 3d idealized squall line simulations, the ML-based P3-like scheme provides a more realistic extended stratiform region when compared to the standard two-moment bulk scheme in ICON. In a realistic case study, the ML-based scheme runs stably, but can not significantly improve the results. This shows that machine learning can be used to coarse-grain super-particle simulations to a bulk scheme of arbitrary complexity.