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The aim is to explore nonlinear model reduction methods effective in transport-dominated scenarios, particularly where linear approaches fail.

July 3, 2026Open Access

Nonlinear model reduction for transport-dominated problems

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The aim is to explore nonlinear model reduction methods effective in transport-dominated scenarios, particularly where linear approaches fail.
Surveyed various nonlinear model reduction techniques.
Categorized techniques into transformation-based methods, online adaptive techniques, and formulations combining nonlinear parametrizations with residual minimization.
Emphasized three elements: nonlinear parametrizations, reduced dynamics, and online solvers.
Identified nonlinear methods that outperform linear approximations in transport-dominated problems.
Classified approaches enhance understanding of effective modeling in intricate dynamic systems.

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Survey highlights nonlinear model reduction techniques for effective transport-dominated problem-solving, indicating potential efficiencies.

Hesthaven et al. (2026) studied this question.

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Survey highlights nonlinear model reduction techniques for effective transport-dominated problem-solving, indicating potential efficiencies.