Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular value decomposition (cSVD) or the SVD-like decomposition have been developed for preserving Hamiltonian structure during MOR. In this contribution, we show how symplectic structure preserving basis generation can be made more efficient with randomized matrix factorizations. We present a randomized complex SVD (rcSVD) algorithm and a randomized SVD-like decomposition (rSVD-like). We demonstrate the efficiency of the approaches with numerical experiments on high dimensional systems.
%0 Conference Paper
%1 10.1007/978-3-031-56208-2_9
%A Herkert, R.
%A Buchfink, P.
%A Haasdonk, B.
%A Rettberg, J.
%A Fehr, J.
%B Large-Scale Scientific Computations
%C Cham
%D 2024
%E Lirkov, Ivan
%E Margenov, Svetozar
%I Springer Nature Switzerland
%K EXC2075 PN3 PN3A-8 PN5 PN5-7 PN6 PN6-1(II) curated
%P 99--107
%T Randomized Symplectic Model Order Reduction for Hamiltonian Systems
%X Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular value decomposition (cSVD) or the SVD-like decomposition have been developed for preserving Hamiltonian structure during MOR. In this contribution, we show how symplectic structure preserving basis generation can be made more efficient with randomized matrix factorizations. We present a randomized complex SVD (rcSVD) algorithm and a randomized SVD-like decomposition (rSVD-like). We demonstrate the efficiency of the approaches with numerical experiments on high dimensional systems.
%@ 978-3-031-56208-2
@inproceedings{10.1007/978-3-031-56208-2_9,
abstract = {Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular value decomposition (cSVD) or the SVD-like decomposition have been developed for preserving Hamiltonian structure during MOR. In this contribution, we show how symplectic structure preserving basis generation can be made more efficient with randomized matrix factorizations. We present a randomized complex SVD (rcSVD) algorithm and a randomized SVD-like decomposition (rSVD-like). We demonstrate the efficiency of the approaches with numerical experiments on high dimensional systems.},
added-at = {2024-10-15T17:23:57.000+0200},
address = {Cham},
author = {Herkert, R. and Buchfink, P. and Haasdonk, B. and Rettberg, J. and Fehr, J.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21eb2bb4951a0104ba400e5f9529ce502/simtech},
booktitle = {Large-Scale Scientific Computations},
editor = {Lirkov, Ivan and Margenov, Svetozar},
interhash = {e9d1b612a6b17d90226f0f74c57a399e},
intrahash = {1eb2bb4951a0104ba400e5f9529ce502},
isbn = {978-3-031-56208-2},
keywords = {EXC2075 PN3 PN3A-8 PN5 PN5-7 PN6 PN6-1(II) curated},
pages = {99--107},
publisher = {Springer Nature Switzerland},
timestamp = {2025-01-27T13:14:14.000+0100},
title = {Randomized Symplectic Model Order Reduction for Hamiltonian Systems},
year = 2024
}
