Uncertainty Modeling in Physical and Biological Systems

With large-scale simulation reaching some degree of maturity
we pose the more general question how to model uncertainty in
physical and biological systems and how to propagate it. 
To this end, we propose 
a multi-element generalized Polynomial Chaos (ME-gPC) method that
can overcome the difficulties associated with long-term integration,
stochastic bifurcations and strong nonlinearities typically encountered
in unsteady problems. 

Specifically, we extend the pioneering ideas of Norbert Wiener 
on polynomial chaos and our previous work on Wiener-Askey expansions
in order to handle stochastic inputs
with arbitrary probability distributions, either continuous or
discrete. This fundamental development, in turn, allows us to
introduce a subdomain decomposition of the random space, thus 
resolving adaptively large levels of localized random fluctuations and 
even stochastic discontinuities.