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arXiv · 2602.01397

Nonlinear model reduction for transport-dominated problems

Jan S. Hesthaven·Benjamin Peherstorfer·Benjamin Unger
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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.

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Jan S. Hesthaven, Benjamin Peherstorfer, Benjamin Unger. 2026-02-01. Nonlinear model reduction for transport-dominated problems. https://arxiv.org/abs/2602.01397

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