# Sparsity-promoting dynamic mode decomposition

arXiv: https://arxiv.org/abs/1309.4165 · HTML: https://mlsanity.com/paper/1309.4165/

## Key facts

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

## Built on by (most cited first, 30 of 30)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Residual Dynamic Mode Decomposition: Robust and verified Koopmanism](https://mlsanity.com/paper/2205.09779/) (2022)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems](https://mlsanity.com/paper/2209.02244/) (2022)
- [Koopman operator learning using invertible neural networks](https://mlsanity.com/paper/2306.17396/) (2023)
- [Interpreting and generalizing deep learning in physics-based problems with functional linear models](https://mlsanity.com/paper/2307.04569/) (2023)
- [Dynamical systems and complex networks: A Koopman operator perspective](https://mlsanity.com/paper/2405.08940/) (2024)
- [An Introductory Guide to Koopman Learning](https://mlsanity.com/paper/2510.22002/) (2025)
- [Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data](https://mlsanity.com/paper/2107.11999/) (2021)
- [Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations](https://mlsanity.com/paper/2104.14034/) (2021)
- [Gaussian Process Koopman Mode Decomposition](https://mlsanity.com/paper/2209.04111/) (2022)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [Nonparametric Sparse Online Learning of the Koopman Operator](https://mlsanity.com/paper/2405.07432/) (2024)
- [Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections](https://mlsanity.com/paper/2102.09973/) (2021)
- [Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction](https://mlsanity.com/paper/2202.11432/) (2022)
- [Digital Twin Data Modelling by Randomized Orthogonal Decomposition and Deep Learning](https://mlsanity.com/paper/2206.08659/) (2022)
- [A Data-driven Approach for Rapid Detection of Aeroelastic Modes from Flutter Flight Test Based on Limited Sensor Measurements](https://mlsanity.com/paper/2403.11521/) (2024)
- [Invertible Koopman neural operator for data-driven modeling of partial differential equations](https://mlsanity.com/paper/2503.19717/) (2025)
- [Dynamic Modes as Time Representation for Spatiotemporal Forecasting](https://mlsanity.com/paper/2506.01212/) (2025)
- [Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Data](https://mlsanity.com/paper/2312.12113/) (2023)
- [Non-negative Subspace Feature Representation for Few-shot Learning in Medical Imaging](https://mlsanity.com/paper/2404.02656/) (2024)
- [Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems](https://mlsanity.com/paper/2410.16656/) (2024)
- [Nonparametric Sparse Online Learning of the Koopman Operator](https://mlsanity.com/paper/2501.16489/) (2025)
- [Avoiding spectral pollution for transfer operators using residuals](https://mlsanity.com/paper/2507.16915/) (2025)
- [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025)
- [Spatially Aware Dictionary-Free Koopman Eigenfunction Identification for Modeling and Control](https://mlsanity.com/paper/2511.22648/) (2025)
- [Comprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction](https://mlsanity.com/paper/2601.11116/) (2026)
- [A neural operator framework for data-driven discovery of stability and receptivity in physical systems](https://mlsanity.com/paper/2604.19465/) (2026)
- [Learning Generalizable Reconstruction of High-Dimensional Neural Dynamics](https://mlsanity.com/paper/2608.16569/) (2026)

## 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.