mlsanityData to 7 Oct 2026

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

arXiv 2605.14224 ↗First posted 14 May 2026math.NA cs.AI cs.NAcited by 1

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Abstract (arXiv)

We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, 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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 10 of its 55 references that are in the map. First posted on arXiv 14 May 2026.

Builds on

10 of 55 references.

References · 10

  1. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  2. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 142
  3. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  4. 2019Data-driven approximation of the Koopman generator: Model reduction, system identification, and controlcited by 85
  5. 2021Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systemscited by 44
  6. 2022The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systemscited by 21
  7. 2024Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operatorscited by 7
  8. 2020Koopman Resolvent: A Laplace-Domain Analysis of Nonlinear Autonomous Dynamical Systemscited by 4
  9. 2014Quadrature-Based Vector Fitting: Implications For H2 System Approximationcited by 3
  10. 2021A wavelet-based dynamic mode decomposition for modeling mechanical systems from partial observationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networkscited by 0