mlsanityData to 14 Oct 2026

Sparsity-promoting dynamic mode decomposition

arXiv 1309.4165 ↗First posted 17 Sep 2013physics.flu-dyn math.DS math.OCcited by 30

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Abstract (arXiv)

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. In our method, sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the ℓ1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

Key facts. Cited by 30 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Sep 2013.

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Citing papers per year: 2021: 6; 2022: 6; 2023: 3; 2024: 5; 2025: 7; 2026: 3.

30 papers.

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  1. 2021Modern Koopman Theory for Dynamical Systemscited by 276
  2. 2021Deeptime: a Python library for machine learning dynamical models from time series datacited by 38
  3. 2022Residual Dynamic Mode Decomposition: Robust and verified Koopmanismcited by 36
  4. 2021Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantificationcited by 30
  5. 2022The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systemscited by 21
  6. 2023Koopman operator learning using invertible neural networkscited by 12
  7. 2023Interpreting and generalizing deep learning in physics-based problems with functional linear modelscited by 9
  8. 2024Dynamical systems and complex networks: A Koopman operator perspectivecited by 9
  9. 2025An Introductory Guide to Koopman Learningcited by 6
  10. 2021Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Datacited by 4
  11. 2021Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulationscited by 3
  12. 2022Gaussian Process Koopman Mode Decompositioncited by 3
18 more
  1. 2022Physics-Informed Koopman Networkcited by 2
  2. 2024Nonparametric Sparse Online Learning of the Koopman Operatorcited by 2
  3. 2021Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collectionscited by 1
  4. 2022Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal predictioncited by 1
  5. 2022Digital Twin Data Modelling by Randomized Orthogonal Decomposition and Deep Learningcited by 1
  6. 2024A Data-driven Approach for Rapid Detection of Aeroelastic Modes from Flutter Flight Test Based on Limited Sensor Measurementscited by 1
  7. 2025Invertible Koopman neural operator for data-driven modeling of partial differential equationscited by 1
  8. 2025Dynamic Modes as Time Representation for Spatiotemporal Forecastingcited by 1
  9. 2023Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Datacited by 0
  10. 2024Non-negative Subspace Feature Representation for Few-shot Learning in Medical Imagingcited by 0
  11. 2024Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systemscited by 0
  12. 2025Nonparametric Sparse Online Learning of the Koopman Operatorcited by 0
  13. 2025Avoiding spectral pollution for transfer operators using residualscited by 0
  14. 2025Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structurescited by 0
  15. 2025Spatially Aware Dictionary-Free Koopman Eigenfunction Identification for Modeling and Controlcited by 0
  16. 2026Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reductioncited by 0
  17. 2026A neural operator framework for data-driven discovery of stability and receptivity in physical systemscited by 0
  18. 2026Learning Generalizable Reconstruction of High-Dimensional Neural Dynamicscited by 0