# Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems

arXiv: https://arxiv.org/abs/2410.16656 · HTML: https://mlsanity.com/paper/2410.16656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 51 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Data-driven local operator finding for reduced-order modelling of plasma systems: I. Concept and verifications](https://mlsanity.com/paper/2403.01523/) (2024)
- [Data-driven local operator finding for reduced-order modelling of plasma systems: II. Application to parametric dynamics](https://mlsanity.com/paper/2403.01532/) (2024)
- [Multi-resolution Dynamic Mode Decomposition for Damage Detection in Wind Turbine Gearboxes](https://mlsanity.com/paper/2110.04103/) (2021)
- [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)

## Abstract (arXiv)

This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating time-delay embedding and leveraging Orthogonal Matching Pursuit (OMP), parsDMD ensures robustness against noise and effectively handles complex, nonlinear dynamics. The algorithm is validated on a diverse range of datasets, including standing wave signals, identifying hidden dynamics, fluid dynamics simulations (flow past a cylinder and transonic buffet), and atmospheric sea-surface temperature (SST) data. ParsDMD addresses a significant limitation of the traditional sparsity-promoting DMD (spDMD), which requires manual tuning of sparsity parameters through a rigorous trial-and-error process to balance between single-mode and all-mode solutions. In contrast, parsDMD autonomously determines the optimally sparse subset of modes without user intervention, while maintaining minimal computational complexity. Comparative analyses demonstrate that parsDMD consistently outperforms spDMD by providing more accurate mode identification and effective reconstruction in noisy environments. These advantages render parsDMD an effective tool for real-time diagnostics, forecasting, and reduced-order model construction across various disciplines.