The mapping-based methods (γ-SQC and spin-LSC), again, show more accurate results that are comparable to the HEOM method, and the steady-state population for the upper polariton is also similar to the HEOM method. We also observe that the transitions into the dark states are better captured with the mapping-based methods, although the γ-SQC method outperforms the spin-LSC method again in predicting the longer time transitions from the dark states to the lower polariton states. Further, we note that the population of the lower polariton state computed via the γ-SQC method is comparable to the populations predicted from the HEOM method, while the population of the lower polariton state computed from the spin-LSC method is consistently lower than that from the HEOM method.