# Randomized Projection Learning Method forDynamic Mode Decomposition

arXiv: https://arxiv.org/abs/2110.01718 · HTML: https://mlsanity.com/paper/2110.01718/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Data-driven reduced-order models via regularized operator inference for a single-injector combustion process](https://mlsanity.com/paper/2008.02862/) (2020)
- [Experiments with Random Projection](https://mlsanity.com/paper/1301.3849/) (2013)
- [Sparsity-promoting algorithms for the discovery of informative Koopman invariant subspaces](https://mlsanity.com/paper/2002.10637/) (2020)
- [Geometric Considerations of a Good Dictionary for Koopman Analysis of Dynamical Systems: Cardinality, 'Primary Eigenfunction,' and Efficient Representation](https://mlsanity.com/paper/1912.09570/) (2019)

## Built on by (most cited first, 2 of 2)

- [Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition](https://mlsanity.com/paper/2311.01377/) (2023)
- [RANDSMAPs: Random-Feature/multi-Scale Neural Decoders with Mass Preservation](https://mlsanity.com/paper/2601.14794/) (2026)

## Abstract (arXiv)

A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension. Keyword: Koopman Operator, Dynamic Mode Decomposition(DMD), Johnson-Lindenstrauss Lemma, Random Projection, Data-driven method.