Optimization-Based Combined Reduction for Nonlinear Systems

In applications requiring model-constrained optimization, model reduction may be indispensable to facilitate an acceptable timescale for the solution. For models with high-dimensional state- and also high-dimensional parameter-spaces the optimization is impeded twice. First, due to the high-dimensional parameter-space many solutions for varying locations in the parameter-space are usually required, second, each of these solutions is costly due to the high-dimensional state-space. A combined state- and parameter-space reduction as proposed in [1] can adress these issues. This combined reduction relies on a greedy sampling of the parameter-space to iteratively assemble a low-dimensional parameter base and a POD-based reduction at locations of the parameter base components. Yet, the greedy algorithm still requires the sampling in the high-dimensional parameter-space. An extensions to this algorithm is proposed in [2], which uses a Monte-Carlo approach to select low-dimensional “hyper”-bases for the parameter-space over which the greedy sampling is performed. And since this combined reduction only requires solutions of the associated model, it is generally applicable also to nonlinear system, which will be demonstrated.