Nonlinear model reduction for transport-dominated problems
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 39 of its 226 references that are in the map. First posted on arXiv 1 Feb 2026.
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