State-preserving Nonlinear Model Reduction Procedure

Model reduction has proven to be a powerful tool to deal with challenges arising from large-scale models. This is also reflected in the large number of different reduction techniques that have been developed. Most of these methods focus on minimizing the approximation error, however, they usually result in a loss of physical interpretability of the reduced model. A new reduction technique which preserves a non-prescribed subset of the original state variables in the reduced model is presented in this work. The technique is derived from the Petrov-Galerkin projection by adding constraints on the projection matrix. This results in a combinatorial problem of which states need to be selected. A sequential algorithm has been developed based on the modified Gram-Schmidt orthogonalization procedure. The presented technique is applied to two examples where the reduction error is found to be comparable to the traditional POD method. At the same time, the technique has the advantage that the physical interpretation of the remaining states is retained.