Model Reduction for Transport-Dominated Problems via Cross-Correlation Based Snapshot Registration

TL;DR

This paper introduces a novel model reduction technique for transport-dominated problems that uses cross-correlation based snapshot registration to improve the efficiency and accuracy of linear approximation methods.

Contribution

The paper presents a complete framework employing cross-correlation based snapshot registration to accelerate Kolmogorov n-width decay for better reduced-order models.

Findings

Effective in 1D travelling waves

Improves accuracy in 2D vortex case

Speeds up model reduction process

Abstract

Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and inaccurate reduced-order models. In this work, we propose a model reduction approach for transport-dominated problems by employing cross-correlation based snapshot registration to accelerate the Kolmogorov $n$-width decay, thereby enabling the construction of efficient and accurate reduced-order models using linear approximation methods. We propose a complete framework comprising offline-online stages for the development of reduced order models using the cross-correlation based snapshots registration. The effectiveness of the proposed approach is demonstrated using two test cases: 1D travelling waves and the higher-order methods benchmark test case, 2D isentropic convective vortex.