# Koopman Ensembles for Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2403.06757 · HTML: https://mlsanity.com/paper/2403.06757/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 13 of 13)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Maximizing Overall Diversity for Improved Uncertainty Estimates in Deep Ensembles](https://mlsanity.com/paper/1906.07380/) (2019)
- [Neural Koopman prior for data assimilation](https://mlsanity.com/paper/2309.05317/) (2023)
- [Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data](https://mlsanity.com/paper/2303.06972/) (2023)
- [Calibration of wind speed ensemble forecasts for power generation](https://mlsanity.com/paper/2104.14910/) (2021)
- [Learning Sentinel-2 reflectance dynamics for data-driven assimilation and forecasting](https://mlsanity.com/paper/2305.03743/) (2023)

## Built on by (most cited first, 1 of 1)

- [Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecasting](https://mlsanity.com/paper/2609.37435/) (2026)

## Abstract (arXiv)

In the context of an increasing popularity of data-driven models to represent dynamical systems, many machine learning-based implementations of the Koopman operator have recently been proposed. However, the vast majority of those works are limited to deterministic predictions, while the knowledge of uncertainty is critical in fields like meteorology and climatology. In this work, we investigate the training of ensembles of models to produce stochastic outputs. We show through experiments on real remote sensing image time series that ensembles of independently trained models are highly overconfident and that using a training criterion that explicitly encourages the members to produce predictions with high inter-model variances greatly improves the uncertainty quantification of the ensembles.