Information sharing-based multivariate proper orthogonal decomposition

Abstract

This study explores challenges in multivariate modal decomposition for various flow scenarios, emphasizing the problem of inconsistent physical modes in Proper Orthogonal Decomposition (POD). This inconsistency arises due to POD's inability to capture inter-variable relationships and common flow patterns, resulting in a loss of phase information. To address this issue, the study introduces two novel data-driven modal analysis methods, collectively called Information Sharing-Based Multivariate POD (IMPOD). These methods, namely, Shared Space Information Multivariate POD (SIMPOD) and Shared Time Information Multivariate POD (TIMPOD), aim to regularize modal decomposition by promoting information sharing among variables. TIMPOD, which assumes shared time information, successfully aligns multivariate modes and corrects their phases without significantly affecting reconstruction error, making it a promising corrective technique for multivariate modal decomposition. In contrast, SIMPOD, which assumes shared space information, reorders modes and may lead to a loss of meaningful insight and reconstruction error.