Geometric Optimization for Structure-Preserving Model Reduction of Hamiltonian Systems

Classical model reduction methods disregard the special symplectic structure associated with Hamiltonian systems. A key challenge in projection-based approaches is to construct a sym-plectic basis that captures essential system information. This necessitates computation of so-called proper decomposition (PSD) given sample data set. The PSD problem allows for canonical formulation as an optimization on Stiefel manifold. However, their Euclidean counterparts, projectors only depend underlying subspaces and not selected bases. motivates tackle Riemannian Grassmann manifold, i.e., matrix manifold projectors. Initial investigations this feature recent preprint authors. In work, we investigate feasibility performance approach two academic numerical examples. More precisely, calculate optimized snapshot matrices stem from solving one-dimensional linear wave equation nonlinear Schrödinger equation.