发表机构
University of Cambridge（剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出等变谱子流形（eSSM）降阶算法，利用全阶模型对称性提升计算速度与模型鲁棒性，在基准问题上验证了其相比传统SSM降阶的优势。
AI 中文摘要
谱子流形（Spectral Submanifold，SSM）降阶是一种数学上严谨的可靠非线性降阶模型构建途径，可捕捉动态模态分解（Dynamic Mode Decomposition，DMD）等线性技术无法覆盖的动力学特性。然而，SSM的计算仍存在计算成本过高的问题，尤其针对高维系统。本研究提出等变谱子流形（equivariant spectral submanifold，eSSM）降阶，这是SSM框架的新型扩展，在降阶过程中明确纳入全阶模型的对称性。我们通过证明SSM天然是等变子流形，且相关图表与降阶动力学继承合适的诱导群作用，建立该方法的数学基础。基于此框架，我们开发新型等变SSM降阶算法，利用这些对称性大幅提升计算速度，同时增强模型鲁棒性。我们在多个基准问题（包括科学领域通用任务框架测试）上验证了该方法的优势。
英文摘要
Spectral submanifold (SSM) reduction has emerged as a mathematically principled route to reliable nonlinear reduced-order models, capturing dynamics beyond the reach of linear techniques such as Dynamic Mode Decomposition (DMD). The computation of SSMs, however, remains computationally expensive, particularly for high-dimensional systems. In this work, we introduce equivariant spectral submanifold (eSSM) reduction, a novel extension of the SSM framework that explicitly incorporates symmetries of the full-order model into the reduction process. We establish the mathematical foundations of this approach by showing that SSMs are naturally equivariant submanifolds and that the associated charts and reduced dynamics inherit the appropriate induced group actions. Building on this framework, we develop a novel equivariant SSM reduction algorithm that exploits these symmetries to achieve substantially faster computations while also improving model robustness. We demonstrate the advantages of this approach on several benchmark problems including a test from the Common Task Framework for Science.
