Nonlinear model reduction for transport-dominated problems
This work tackles the challenge of model reduction for transport-dominated problems, which is important for computational science and engineering, but it is incremental as it surveys existing methods.
The article surveys nonlinear model reduction methods that address the inefficiency of linear approximations in transport-dominated problems with wave-like phenomena and moving coherent structures, organizing techniques around nonlinear parametrizations, reduced dynamics, and online solvers.
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.