27th Conference of the International Linear Algebra Society (ILAS 2026)

Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework

May 19, 2026, 2:25 PM

25m

Torgersen Hall 1020 (Virginia Tech)

Minisymposium Talk Linear Algebra Foundations for Data-driven Modeling and Model Order Reduction Linear Algebra Foundations for Data-driven Modeling and Model Order Reduction

Speaker

Cankat Tilki (Virginia Tech)

Description

We present an in-depth analysis of the Koopman operator using wavelet transform. Based on this analysis, we construct an invariant subspace for the Koopman operator and introduce wavelet-based observables that span this subspace. Moreover, on this subspace, we study the Koopman operator and its eigendecomposition. To approximate its action numerically over this subspace, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables, leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples.