Randomized Symplectic Model Order Reduction for Hamiltonian Systems

2023/03/07 by Robin Herkert, Herkert, Robin, Patrick Buchfink +7
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Parallel Computing and Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2303.04036

openalex publication_date 2023/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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.

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