Weak-DMD: A Galerkin approach to the problem of noise in the Dynamic Mode Decomposition algorithm

Fuente: arXiv
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Hauptverfasser: Bennett, William, McClarren, Ryan G., Smith, Ethan, Derman, Melek
Format: Preprint
Veröffentlicht: 2026
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author Bennett, William
McClarren, Ryan G.
Smith, Ethan
Derman, Melek
author_facet Bennett, William
McClarren, Ryan G.
Smith, Ethan
Derman, Melek
contents Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The standard formulation of DMD is subject to strict assumptions concerning the time-spacing of the snapshots and is biased by measurement noise. Variations on the method have been developed to address these shortcomings, but the problem is still open. Motivated by the effectiveness of Galerkin methods in the field of model discovery, a weak formulation of DMD is presented, weak-DMD. Weak-DMD precludes timestep considerations and also filters noise. Results for two nuclear engineering applications and the flow of fluid past a cylinder are given and compared with a state of the art DMD algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2604_14350
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Weak-DMD: A Galerkin approach to the problem of noise in the Dynamic Mode Decomposition algorithm
Bennett, William
McClarren, Ryan G.
Smith, Ethan
Derman, Melek
Computational Engineering, Finance, and Science
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The standard formulation of DMD is subject to strict assumptions concerning the time-spacing of the snapshots and is biased by measurement noise. Variations on the method have been developed to address these shortcomings, but the problem is still open. Motivated by the effectiveness of Galerkin methods in the field of model discovery, a weak formulation of DMD is presented, weak-DMD. Weak-DMD precludes timestep considerations and also filters noise. Results for two nuclear engineering applications and the flow of fluid past a cylinder are given and compared with a state of the art DMD algorithm.
title Weak-DMD: A Galerkin approach to the problem of noise in the Dynamic Mode Decomposition algorithm
topic Computational Engineering, Finance, and Science
url https://arxiv.org/abs/2604.14350