An optimization framework for goal-oriented, model-based reduction of large-scale systems

Optimization-ready 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-based optimization framework. The mathematical framework permits consideration of general dynamical systems with general parametric variations. The methodology is applicable to both linear and nonlinear systems and to systems with many input parameters. This paper focuses on an initial presentation and demonstration of the methodology on a simple linear model problem of the two-dimensional, time-dependent heat equation with a small number of inputs. For this example, the reduced models determined by the new approach provide considerable improvement over those derived using the proper orthogonal decomposition.