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.
