# Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds

@article{Buchfink2021SymplecticMR, title={Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds}, author={Patrick Buchfink and Silke Glas and Bernard Haasdonk}, journal={ArXiv}, year={2021}, volume={abs/2112.10815} }

Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-nwidths such as certain transport-dominated problems, however, classical linear-subspace reducedorder models (ROMs) of low dimension might yield inaccurate results. Thus, the concept of classical linear-subspace ROMs has to be extended to more general concepts, like Model Order Reduction (MOR) on manifolds. Moreover, as we…

## 2 Citations

Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale mechanical systems

- Computer ScienceArXiv
- 2022

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian mechanical systems that exploits knowledge of the governing equations (but not their discretization) to define the form and parametrization of a Lagrangia ROM which can be learned from projected snapshot data.

Reduced-order modeling for Ablowitz-Ladik equation

- MathematicsArXiv
- 2022

In this paper, reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schr ¨ odinger equation (NLSE) with and without…

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