Nonlinear model reduction for transport-dominated problems
Numerical Analysis
2026-02-03 v1 Machine Learning
Numerical Analysis
Optimization and Control
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.
Cite
@article{arxiv.2602.01397,
title = {Nonlinear model reduction for transport-dominated problems},
author = {Jan S. Hesthaven and Benjamin Peherstorfer and Benjamin Unger},
journal= {arXiv preprint arXiv:2602.01397},
year = {2026}
}