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 the current 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 (rSVD-like) decomposition. We demonstrate the efficiency of the approaches with numerical experiments on high dimensional systems.

翻译：多查询或实时环境中大规模动力系统的仿真需要高效的替代建模技术，例如通过模型降阶（MOR）实现。近期，针对MOR过程中保持哈密顿结构，已发展出如复数奇异值分解（cSVD）或类SVD分解等辛方法。在本文中，我们展示如何通过随机矩阵分解使辛结构保持的基生成更加高效。我们提出了一种随机复数SVD（rcSVD）算法和一种随机类SVD（rSVD-like）分解，并通过高维系统的数值实验证明了这些方法的效率。