Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy

A non-intrusive bifidelity strategy is applied to the computation of statistics of a quantity of interest (QoI) which depends in a non-smooth way upon the stochastic parameters. The procedure leverages the accuracy of a high-fidelity model and the efficiency of a low-fidelity model, obtained through the use of different levels of numerical resolution, to pursue a high quality approximation of the statistics with a moderate number of high-fidelity simulations. The method is applied first to synthetic test cases with outputs exhibiting either a continuous or a discontinuous behaviour, then to the realistic simulation of a flow in an underground network of fractures, whose stochastic geometry outputs a non-smooth QoI. In both applications, the results highlight the efficacy of the approach in terms of error decay versus the number of computed high-fidelity solutions, even when the QoI lacks smoothness. For the underground simulation problem, the observed gain in computational cost is at least of one order of magnitude.