Goal-oriented, model-constrained optimization for reduction of large-scale systems

Optimization-oriented reduced-order models should target a particular output functional, span an applicable range of dynamic and parametric inputs, and respect the underlying governing equations of the system. To achieve this goal, we present an approach for determining a projection basis that uses a goal-oriented, model-constrained optimization framework. The mathematical framework permits consideration of general dynamical systems with general parametric variations and is applicable to both linear and nonlinear systems. Results for a simple linear model problem of the two-dimensional heat equation demonstrate the ability of the goal-oriented approach to target a particular output functional of interest. Application of the methodology to a more challenging example of a subsonic blade row governed by the unsteady Euler flow equations shows a significant advantage of the new method over the proper orthogonal decomposition.