We consider a class of wave propagation models with aleatoric
and epistemic uncertainties. Using mathematical analysis-based,
shape-independent, a priori parameter estimates, we develop offline/online
strategies to compute statistical moments of a key quantity of interest
in such models. We present  an efficient  reduced order model (ROM)
and high performance computing (HPC) framework with analysis for quantifying
aleatoric and epistemic uncertainties in the propagation of waves through
a stochastic media comprising  a large number of three dimensional
particles.
Simulation even for a single deterministic  three dimensional
configuration is inherently difficult because of the large number of
particles.
The aleatoric uncertainty in the model leads to a larger dimensional system
involving three spatial variables and additional stochastic variables.
Accounting for epistemic uncertainty in key parameters  of the input
probability distributions leads to prohibitive computational complexity.
Our hybrid ROM and HPC framework can be used in conjunction with any
computational method to simulate a single particle deterministic wave
propagation model.