Fast Model Order Reduction via Nonlinear Optimization
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This paper proposes a fast Galerkin projection method for model order reduction of large-scale dynamic systems. We first define a novel dynamic optimization problem in which the projection modes are chosen to minimize the difference between the output from the original model and the output from the Galerkin reduced model. Next, we approximate this dynamic optimization problem by a static problem that can be solved efficiently using standard nonlinear optimization algorithms. The solution of the static problem defines a set of suboptimal projection modes that (approximately) maximize the accuracy of the corresponding reduced model. This is different to the well-known proper orthogonal decomposition and Galerkin projection method (POD-Galerkin method), in which the accuracy of the orthogonal state projection, rather than the accuracy of the reduced model’s output, is maximized. We compare the new method with the POD-Galerkin method for a one-dimensional heat transfer system.
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