Construction of Parametrically-Robust CFD-Based Reduced-Order Models for PDE-Constrained Optimization

A method for simultaneously constructing a reduced-order model and using it as a surrogate model to solve a PDE-constrained optimization problem is introduced. A reducedorder model is built for the parameters corresponding to the initial guess of the optimization problem. Since the resulting reduced-order model can be expected to be accurate only in the vicinity of this point in the parameter space, emphasis is placed on constructing this model by searching for regions of high error. These are determined by solving a small, nonlinear program with the objective defined as a linear combination of a residual error indicator and the objective function of the original PDE-constrained optimization problem. The reduced-order model is updated with information from the high-dimensional model in the regions of large error, and the process is repeated with more emphasis placed solving the PDE-constrained optimization problem. The iteration terminates when the optimality conditions of the PDE-constrained optimization problem are satisfied. Application to a standard, nonlinear CFD shape optimization problem shows that the proposed method effectively solves a PDE-constrained optimization problem with very few full CFD simulation queries.