# Learning low-dimensional representations of ensemble forecast fields using autoencoder-based methods

arXiv: https://arxiv.org/abs/2502.04409 · HTML: https://mlsanity.com/paper/2502.04409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 81 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Medical image denoising using convolutional denoising autoencoders](https://mlsanity.com/paper/1608.04667/) (2016)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [SoftAdapt: Techniques for Adaptive Loss Weighting of Neural Networks with Multi-Part Loss Functions](https://mlsanity.com/paper/1912.12355/) (2019)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [A Unified Framework for Implicit Sinkhorn Differentiation](https://mlsanity.com/paper/2205.06688/) (2022)
- [Generative machine learning methods for multivariate ensemble post-processing](https://mlsanity.com/paper/2211.01345/) (2022)
- [Uncertainty quantification for data-driven weather models](https://mlsanity.com/paper/2403.13458/) (2024)
- [Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.03100/) (2024)
- [FuXi-ENS: A machine learning model for medium-range ensemble weather forecasting](https://mlsanity.com/paper/2405.05925/) (2024)
- [Analog ensemble data assimilation and a method for constructing analogs with variational autoencoders](https://mlsanity.com/paper/2006.01101/) (2020)
- [Machine Learning Techniques to Construct Patched Analog Ensembles for Data Assimilation](https://mlsanity.com/paper/2103.00318/) (2021)
- [Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks](https://mlsanity.com/paper/2309.04452/) (2023)
- [Using proper divergence functions to evaluate climate models](https://mlsanity.com/paper/1301.5927/) (2013)
- [Applications of machine learning to predict seasonal precipitation for East Africa](https://mlsanity.com/paper/2409.06238/) (2024)

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

- [Quantile Regression, Variational Autoencoders, and Diffusion Models for Uncertainty Quantification: A Spatial Analysis of Sub-seasonal Wind Speed Prediction](https://mlsanity.com/paper/2510.16958/) (2025)

## Abstract (arXiv)

Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using discrete gridded representations of the physical variables and dynamics. Uncertainties are assessed by running the simulations multiple times, yielding ensembles of simulated fields as a high-dimensional stochastic representation of the forecast distribution. The high-dimensionality and large volume of ensemble datasets poses major computing challenges for subsequent forecasting stages. Data-driven dimensionality reduction techniques could help to reduce the data volume before further processing by learning meaningful and compact representations. However, existing dimensionality reduction methods are typically designed for deterministic and single-valued inputs, and thus cannot handle ensemble data from multiple randomized simulations. In this study, we propose novel dimensionality reduction approaches specifically tailored to the format of ensemble forecast fields. We present two alternative frameworks, which yield low-dimensional representations of ensemble forecasts while respecting their probabilistic character. The first approach derives a distribution-based representation of an input ensemble by applying standard dimensionality reduction techniques in a member-by-member fashion and merging the member representations into a joint parametric distribution model. The second approach achieves a similar representation by encoding all members jointly using a tailored variational autoencoder. We evaluate and compare both approaches in a case study using 10 years of temperature and wind speed forecasts over Europe. The approaches preserve key spatial and statistical characteristics of the ensemble and enable probabilistic reconstructions of the forecast fields.