Nonlinear model reduction for transport-dominated problems
Abstract
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.
Fields of Study & Subjects
Model Reduction and Neural Networks
Advanced Numerical Methods in Computational Mathematics
Matrix Theory and Algorithms
Publication details
- Journal / source
- Acta Numerica
- Publisher
- Cambridge University Press (CUP)
- Volume
- 35
- Pages
- 173–272
- Publication date
- 19 June 2026
- Language
- EN