A Goal-Oriented Adaptive Sampling Procedure for Projection-Based Reduced-Order Models with Hyperreduction

Projection-based reduced-order models (PROMs) have demonstrated accuracy, reliability, and robustness in approximating high-dimensional, differential equation-based computational models across many applications. For this reason, it has been proposed as a tool for high-querying parametric design problems like those arising in modern aircraft design. Since aerodynamic simulations can be computationally expensive, PROMs offer the potential for more rapid estimations of high-fidelity solutions. However, the efficiency can still be tied to the dimension of the full-order model (FOM), particularly when projected quantities must be frequently recomputed due to non-linearities or parameter dependence. In the case of Petrov-Galerkin models, the projected residual and Jacobian are re-evaluated at every Newton iteration, thereby limiting the anticipated cost improvements. Hyperreduction is one of the tools available to approximate these quantities and address this issue. This work tests the energy-conserving sampling and weighting (ECSW) method as a potential approach for hyperreduction. It will be incorporated into the work in a previous article {10.1016/j.compfluid.2025.106568} which had developed an adaptive sampling procedure for building a reduced-order model (ROM) with a controlled functional error. The impacts of hyperreduction on computational cost and accuracy will be studied using the NACA0012 airfoil.