发表机构
Tsinghua University; Max Planck Institute for Dynamics of Complex Technical Systems（清华大学; 马克斯·普朗克复杂技术系统动力学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出迭代主动子空间（IAS）方法，用于高维参数空间参数化系统的模型降阶，以平衡精度与模型规模，相比原始主动子空间方法获得显著计算增益。
AI 中文摘要
设计和制造中日益增长的复杂性，推动了对具有大维参数空间的快速建模问题的先进技术的需求。在此类背景下，既要避免使用高保真有限元模型，又要实现快速且准确的仿真，颇具挑战性。参数化模型降阶（pMOR）近年来引起了广泛关注。然而，参数空间中的维数灾难严重限制了其有效性。主动子空间（AS）方法已成功应用于具有众多参数的系统的pMOR。但对于高维参数空间的此类系统，降阶模型的精度与紧凑性之间的平衡仍然存在问题，这常常导致模型要么不够小，要么不够精确。在本文中，我们提出了一种用于参数化模型降阶的迭代主动子空间（IAS）方法，该方法在一定程度上解决了精度与降阶模型规模之间的权衡问题，并且与原始主动子空间方法相比，实现了显著的计算增益。
英文摘要
The increasing complexity in design and manufacturing has driven the need for advanced techniques for fast modeling problems with large-dimensional parameter spaces. Avoiding high-fidelity finite element models while achieving fast and accurate simulations in such contexts is challenging. Parametric model order reduction (pMOR) has drawn significant attention in recent years. Nevertheless, the curse of dimensionality in parameter spaces has severely limited its effectiveness. The active subspace (AS) approach has been successfully applied to pMOR for systems with many parameters. However, the balance between accuracy and compactness of the reduced model remains problematic for such systems with high-dimensional parameter spaces. It often results in models that are either not small enough or not accurate enough. In this paper, we propose an iterative active subspace (IAS) approach for parametric model order reduction, which, to some extent, addresses the trade-off between accuracy and reduced model size and achieves substantial computational gains compared to the original active subspace method.
Comments24 pages, 9 figures
