A High-Performance Embedded Hybrid Methodology for Uncertainty Quantification With Applications
Multiphysics processes modeled by a system of unsteady differential equations are naturally suited for partitioned (modular) solution strategies. We consider such a model where probabilistic uncertainties are present in each module of the system and represented as a set of random input parameters. A straightforward approach in quantifying uncertainties in the predicted solution would be to sample all the input parameters into a single set, and treat the full system as a black-box. Although this method is easily parallelizable and requires minimal modifications to deterministic solver, it is blind to the modular structure of the underlying multiphysical model. On the other hand, using spectral representations polynomial chaos expansions (PCE) can provide richer structural information regarding the dynamics of these uncertainties as they propagate from the inputs to the predicted output, but can be prohibitively expensive to implement in the high-dimensional global space of uncertain parameters. Therefore, we investigated hybrid methodologies wherein each module has the flexibility of using sampling or PCE based methods of capturing local uncertainties while maintaining accuracy in the global uncertainty analysis. For the latter case, we use a conditional PCE model which mitigates the curse of dimension associated with intrusive Galerkin or semi-intrusive Pseudospectral methods. After formalizing the theoretical framework, we demonstrate our proposed method using a numerical viscous flow simulation and benchmark the performance against a solely Monte-Carlo method and solely spectral method.