Fig. presents the population dynamics of the polariton states and the dark states for model 2, where the light-matter detuning ω c -ω a -λ varies from negative to positive values, while keeping the other parameters fixed. In Fig. , all trajectory-based methods are able to qualitatively account for the relaxation of the upper polariton state into the other states. However, both MQC methods (Ehrenfest and GFSH) predict a slower relaxation rate and a larger steady-state population for the upper polariton state compared to the HEOM results. Looking at the transitions into and out of the dark states, we observe that both MQC methods are only able to quali-tatively capture the increase in the total dark state populations due to relaxation from the upper polariton state in the short time regime (up to 0.1 ps). One exception to this observation about the dark states is given in Fig. , where the GFSH method predicts comparable dark state populations compared to the HEOM method for negative detuning (ω c -ω a -λ = -200 meV). For the lower polariton populations, both MQC methods consistently underestimate the populations compared to the HEOM method.