# Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed

arXiv: https://arxiv.org/abs/2508.16686 · HTML: https://mlsanity.com/paper/2508.16686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Swin2SR: SwinV2 Transformer for Compressed Image Super-Resolution and Restoration](https://mlsanity.com/paper/2209.11345/) (2022)
- [Application of Deep Convolutional Neural Networks for Detecting Extreme Weather in Climate Datasets](https://mlsanity.com/paper/1605.01156/) (2016)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [UQGAN: A Unified Model for Uncertainty Quantification of Deep Classifiers trained via Conditional GANs](https://mlsanity.com/paper/2201.13279/) (2022)
- [Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed](https://mlsanity.com/paper/2203.09179/) (2022)
- [Wind speed super-resolution and validation: from ERA5 to CERRA via diffusion models](https://mlsanity.com/paper/2401.15469/) (2024)
- [Algorithmic Hallucinations of Near-Surface Winds: Statistical Downscaling with Generative Adversarial Networks to Convection-Permitting Scales](https://mlsanity.com/paper/2302.08720/) (2023)
- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [Capturing Climatic Variability: Using Deep Learning for Stochastic Downscaling](https://mlsanity.com/paper/2406.02587/) (2024)
- [An analytic comparison of regularization methods for Gaussian Processes](https://mlsanity.com/paper/1602.00853/) (2016)
- [Statistical treatment of convolutional neural network super-resolution of inland surface wind for subgrid-scale variability quantification](https://mlsanity.com/paper/2211.16708/) (2022)

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

- [Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries](https://mlsanity.com/paper/2604.02520/) (2026)

## Abstract (arXiv)

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic uncertainty, few offer closed-form, multidimensional distributions that preserve spatial correlation while remaining computationally tractable. In this work, we present a framework for training neural networks with a multidimensional Gaussian loss, generating closed-form predictive distributions over outputs with non-identically distributed and heteroscedastic structure. Our approach captures aleatoric uncertainty by iteratively estimating the means and covariance matrices, and is demonstrated on a super-resolution example. We leverage a Fourier representation of the covariance matrix to stabilize network training and preserve spatial correlation. We introduce a novel regularization strategy -- referred to as information sharing -- that interpolates between image-specific and global covariance estimates, enabling convergence of the super-resolution downscaling network trained on image-specific distributional loss functions. This framework allows for efficient sampling, explicit correlation modeling, and extensions to more complex distribution families all without disrupting prediction performance. We demonstrate the method on a surface wind speed downscaling task and discuss its broader applicability to uncertainty-aware prediction in scientific models.