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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. |
