SparseModesNet uses POD linear encoding with LassoNet-enforced sparse nonlinear NN decoding to select modes and reduce reconstruction error by 51-78% versus polynomial manifold methods on turbulent channel flow while preserving interpretability.
Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework
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abstract
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.
fields
physics.flu-dyn 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
SparseModesNet uses POD linear encoding with LassoNet-enforced sparse nonlinear NN decoding to select modes and reduce reconstruction error by 51-78% versus polynomial manifold methods on turbulent channel flow while preserving interpretability.