Combine GMG reduction with nonlinear approximation maps

Develop a model-reduction method that combines generalized manifold Galerkin reduction for port-Hamiltonian systems with a nonlinear approximation map, extending the linear-approximation-map setting considered in the paper.

Background

The proposed GMG-POD-NN-ROM uses a two-step procedure: generalized manifold Galerkin reduction followed by a neural-network approximation of the reduced state-dependent interconnection and dissipation matrices. Although the generalized manifold Galerkin framework can accommodate general nonlinear approximation maps, the paper restricts its construction and numerical investigation to linear approximation maps. Extending the method to the combination of GMG reduction and nonlinear approximation maps is therefore identified as a concrete direction for future work.