Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911879214923776 |
|---|---|
| author | Herkert, Robin Buchfink, Patrick Haasdonk, Bernard Rettberg, Johannes Fehr, Jörg |
| author_facet | Herkert, Robin Buchfink, Patrick Haasdonk, Bernard Rettberg, Johannes Fehr, Jörg |
| contents | Solving high-dimensional dynamical systems in multi-query or real-time applications requires efficient surrogate modelling techniques, as e.g., achieved via model order reduction (MOR). If these systems are Hamiltonian systems their physical structure should be preserved during the reduction, which can be ensured by applying symplectic basis generation techniques such as the complex SVD (cSVD). Recently, randomized symplectic methods such as the randomized complex singular value decomposition (rcSVD) have been developed for a more efficient computation of symplectic bases that preserve the Hamiltonian structure during MOR. In the current paper, we present two error bounds for the rcSVD basis depending on the choice of hyperparameters and show that with a proper choice of hyperparameters, the projection error of rcSVD is at most a constant factor worse than the projection error of cSVD. We provide numerical experiments that demonstrate the efficiency of randomized symplectic basis generation and compare the bounds numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems Herkert, Robin Buchfink, Patrick Haasdonk, Bernard Rettberg, Johannes Fehr, Jörg Numerical Analysis Solving high-dimensional dynamical systems in multi-query or real-time applications requires efficient surrogate modelling techniques, as e.g., achieved via model order reduction (MOR). If these systems are Hamiltonian systems their physical structure should be preserved during the reduction, which can be ensured by applying symplectic basis generation techniques such as the complex SVD (cSVD). Recently, randomized symplectic methods such as the randomized complex singular value decomposition (rcSVD) have been developed for a more efficient computation of symplectic bases that preserve the Hamiltonian structure during MOR. In the current paper, we present two error bounds for the rcSVD basis depending on the choice of hyperparameters and show that with a proper choice of hyperparameters, the projection error of rcSVD is at most a constant factor worse than the projection error of cSVD. We provide numerical experiments that demonstrate the efficiency of randomized symplectic basis generation and compare the bounds numerically. |
| title | Error Analysis of Randomized Symplectic Model Order Reduction for Hamiltonian systems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.10465 |