Nonlinear model reduction of the Navier-Stokes-Equations

Abstract

In this paper three different methods for nonlinear dimensionality reduction are examined: Sammon mapping, Laplacian eigenmaps and autoencoder. These are extended such that they fit in the framework of snapshot based model reduction of flow problems and can be effectively combined with the Galerkin projection. All three methods are compared to the Proper Orthogonal Decomposition as standard benchmark of model reduction. For the Navier-Stokes-Equations especially the Laplacian Eigenmaps can increase the quality of the reduced order model significantly.