Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models

We investigate uncertainty propagation in the context of high-end complex simulation codes, whose runtime on one configuration is on the order of the total limit of computational resources. To this end, we study the use of lower-fidelity data generated by proper orthogonal decomposition-based model reduction. A Gaussian process approach is used to model the difference between the higher-fidelity and the lower-fidelity data. The approach circumvents the extensive sampling of model outputs – impossible in our context – by substituting abundant, lower-fidelity data in place of high-fidelity data. This enables uncertainty analysis while accounting for the reduction in information caused by the model reduction. We test the approach on Navier-Stokes flow models: first on a simplified code and then using a scalable high-fidelity fluid mechanics solver Nek5000. We demonstrate that the approach can give reasonably accurate while conservative error estimates of important statistics including high quantiles of the drag coefficient.