# Gaussian Process Koopman Mode Decomposition

arXiv: https://arxiv.org/abs/2209.04111 · HTML: https://mlsanity.com/paper/2209.04111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 37 references that are in the map.
- First posted on arXiv 9 Sep 2022.

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

- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [Connections and Equivalences between the Nystr"om Method and Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2106.01121/) (2021)
- [Application of Gaussian Process Regression to Koopman Mode Decomposition for Noisy Dynamic Data](https://mlsanity.com/paper/1911.01143/) (2019)

## Built on by (most cited first, 3 of 3)

- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Modal Analysis of Spatiotemporal Data via Multivariate Gaussian Process Regression](https://mlsanity.com/paper/2403.13118/) (2024)
- [Featurizing Koopman Mode Decomposition For Robust Forecasting](https://mlsanity.com/paper/2312.09146/) (2023)

## Abstract (arXiv)

In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the quantities specified by Koopman mode decomposition, namely, eigenvalues, eigenfunctions, and modes. Our model enables the simultaneous estimation of these quantities and latent variables governed by an unknown dynamical system. Furthermore, we introduce an efficient strategy to estimate the parameters of our model by low-rank approximations of covariance matrices. Applying the proposed model to both synthetic data and a real-world epidemiological dataset, we show that various analyses are available using the estimated parameters.