{"ID":2879982,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.16686","arxiv_id":"2508.16686","title":"Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2508.16686","url_pdf":"https://arxiv.org/pdf/2508.16686v1","authors":"[\"Harrison J. Goldwyn\",\"Mitchell Krock\",\"Johann Rudi\",\"Daniel Getter\",\"Julie Bessac\"]","published":"2025-08-21T18:22:44Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ME\",\"stat.ML\"]","methods":"[]","has_code":false}