  A family of semi-intrusive uncertainty propagation (UP) methods for
multiscale models is introduced. The methods are semi-intrusive in the sense
that inspection of the model is limited up to the level of the single scale
systems, and viewing these single scale components as black-boxes. The goal is
to estimate uncertainty in the result of multiscale models at a reduced amount
of time as compared to black-box Monte Carlo (MC). In the resulting
semi-intrusive MC method, the required number of samples of an expensive single
scale model is minimized in order to reduce the execution time for the overall
UP. In the metamodeling approach, the expensive model component is replaced
completely by a computationally much cheaper surrogate model. These
semi-intrusive algorithms have been tested on two case studies based on
reaction-diffusion dynamics. The results demonstrate that the proposed
semi-intrusive methods can result in a significant reduction of the
computational time for multiscale UP, while still computing accurately the
estimates of uncertainties. The semi-intrusive methods can, therefore, be a
valid alternative, when uncertainties of a multiscale model cannot be estimated
by the black-box MC methods in a feasible amount of time.
