LP UP DS 4. Population dynamics of the upper polaritonic state (UP), lower polaritonic state (LP), and sum over all dark states (DS) for the HTC model computed with different MQC dynamics including Ehrenfest, GFSH, γ-SQC, and spin-LSC. Different light-matter coupling strengths (gc = 40.8/68.1/96.1 meV) are used in the dynamics simulations. The number of molecules is Na = 10, the cavity frequency is ωc = 2.0 eV, and the reorganization energy is λ = 30 meV. See Model 3 in Table for details. 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, and the γ-SQC method again outperforms the spin-LSC method in predicting the longer time transitions from the dark states to the lower polariton states. For the population of the lower polariton state, we note that the γ-SQC method tends to overestimate the population compared to the HEOM method, while the spin-LSC method tends to underestimate the population compared to the HEOM method.