Model reduction of traveling-wave problems via Radon cumulative distribution transform

Abstract

Due to their sizeable Kolmogorov n-width, travel-wave problems have brought critical challenges to conventional model reduction techniques. This study aims to provide new insights into this problem by exploiting the Radon cumulative distribution transform (R-CDT) that emerged in the sector of computer vision science. By virtue of the unique property that nonlinear invertible R-CDT renders both traveling and scaling components into amplitude modulations, a substantial model-reduction is achieved in the R-CDT space, while sustaining high accuracy. The method is parameter-free and data-driven, which lends itself to problems regardless of the dimensions or boundary conditions.