Advancements in Reduced Order Model-Based Multifidelity Uncertainty Quantification for High-Speed Flows

This work investigates the efficiency and utility of the reduced-basis method for creating lower-fidelity approximations, such as projection-based reduced-order models (ROMs), within a multifidelity (MF) uncertainty propagation framework. Building on previous work [ 1], we present an offline workflow, where the ROMs in the MF ensemble are pre-trained, and an online/hybrid workflow, where the ROMs are trained as part of the MF resource allocation problem. For this latter case, we propose a novel algorithm that uses data-driven surrogates to aid in solving a resource optimization combining training and sampling costs. Related to online ROM training, we also consider the general model tuning problem [2, 3], involving the determination of optimal ROM hyper-parameters within a bi-level tuning workflow, enhancing the performance of a combined ROM and full-order model (FOM) ensemble in minimizing MF estimator variance. Finally, we also provide results for surrogate-based MF approaches based on polynomial chaos [4], which can provide additional statistical quantities like densities and Sobol’ indices. While the approaches presented in this work are general in nature, demonstrations focus on high-speed flows; in particular, on a forward propagation problem for the HIFiRE-1 test vehicle [5 , 6], in which the turbulence coefficients of the Reynolds-averaged Navier Stokes (RANS) model are assumed to be uncertain.