  Photonic condensates are complex systems exhibiting phase transitions due to
the interaction with their molecular environment. Given the macroscopic number
of molecules that form a reservoir of excitations, numerical simulations are
expensive, even for systems with few cavity modes. We present a systematic
construction of molecular excitation profiles with a clear hierarchical
ordering, such that only modes in the lowest order in the hierarchy directly
affect the cavity photon dynamics. In addition to a substantial gain in
computational efficiency for simulations of photon dynamics, the explicit
spatial shape of the mode profiles offers a clear physical insight into the
competition among the cavity modes for access to molecular excitations.
