# State-Of-The-Art Algorithms For Low-Rank Dynamic Mode Decomposition

arXiv: https://arxiv.org/abs/2108.09160 · HTML: https://mlsanity.com/paper/2108.09160/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 20 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems](https://mlsanity.com/paper/1403.4290/) (2014)
- [Low-Rank Dynamic Mode Decomposition: An Exact and Tractable Solution](https://mlsanity.com/paper/1610.02962/) (2016)
- [Low-rank Approximation of Linear Maps](https://mlsanity.com/paper/1812.09042/) (2018)
- [Generalized Kernel-Based Dynamic Mode Decomposition](https://mlsanity.com/paper/2002.04375/) (2020)

## Abstract (arXiv)

This technical note reviews sate-of-the-art algorithms for linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). While repeating several parts of our article "low-rank dynamic mode decomposition: an exact and tractable solution", this work provides additional details useful for building a comprehensive picture of state-of-the-art methods.