Coupling molecular excitations to a quantized radiation field inside an optical cavity produces a set of lightmatter hybrid states known as polaritons. These polariton states, which are a hybridization of matter excitation and photonic excitation, have shown interesting photophysical properties. In particular, the lightmatter interaction has been shown to effectively reduce the coupling between excitons and phonons, which is commonly referred to as the polaron decoupling effect. This polaron decoupling effect results in an enhanced charge transfer rate constant, 1 reduction of the homogeneous linewidth of spectra, and causes ballistic exciton-polariton transport. In particular, the excitonpolariton coherence lifetime could be significantly prolonged due to reduced coupling with the phonon bath. Linear 9,10 and nonlinear spectroscopy are powerful measurements that provide a fundamental understanding of the photophysics of polariton systems. To capture the essential features of polariton photophysics, one needs to simulate N molecules collectively coupled to the cavity mode, typically using the Holestein-Tavis-Cummings (HTC) model Hamiltonian. Further, one needs to explicitly incorporate exciton energy disorders (inhomogeneous disorder) and dipole orientational disorders for the molecule-cavity coupling interactions. In the typical experimental setup, one couple N = 10 3 -10 4 Nanoplatelet to the cavity, or at least N = 10 6 a) Electronic mail: mmondal@ur.rochester.edu b) Electronic mail: pengfei.huo@rochester.edu organic molecules to one cavity mode. When there is no disorder present in the HTC Hamiltonian, one can in principle take advantage of the permutational symmetry of the problem and solve the problem with a mean field solution or the recently proposed CUT-E approach for the zero-temperature case and with a single high-frequency vibration mode per molecule. With the presence of various disorders (and no apparent symmetry in the system), it is computationally challenging to directly stimulate the polariton dynamics when there are a large N of molecules coupled to the cavity, although there is progress in effectively describing static disorders as energy bins while taking advantage of the symmetry in HTC-type Hamiltonian. The Tensor Train decomposition method in principle could handle HTC-type dynamics with disorders, but remains computationally expensive due to the full quantum mechanical treatment for all degrees of freedom (DOFs).