针对传输主导问题，提出高效非线性降维方法
Nonlinear model reduction for transport-dominated problems
- 基于非线性参数化、降维动力学与在线求解器构建框架
- 突破线性降维在波状结构问题中的效率瓶颈
- 适合处理含移动相干结构的复杂物理系统
本文综述了在传输主导问题（如具有波状现象和移动相干结构）中仍有效的非线性模型降维方法，这类问题常受科莫戈罗夫障碍制约。文章围绕非线性参数化、降维动力学和在线求解器三个核心要素，将现有方法分为三类：基于变换的方法、在线自适应技术，以及结合通用非线性参数化与瞬时残差最小化的形式。
原文摘要 · Abstract (English)
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving coherent structures, which are commonly associated with the Kolmogorov barrier. The article organizes nonlinear model reduction techniques around three key elements -- nonlinear parametrizations, reduced dynamics, and online solvers -- and categorizes existing approaches into transformation-based methods, online adaptive techniques, and formulations that combine generic nonlinear parametrizations with instantaneous residual minimization.
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