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

• URL: http://arxiv.org/abs/2508.16686v1
• Date: Thu, 21 Aug 2025 18:22:44 GMT
• Title: Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed
• Authors: Harrison J. Goldwyn, Mitchell Krock, Johann Rudi, Daniel Getter, Julie Bessac,
• Abstract summary: We present a framework for training neural networks with a multidimensional Gaussian loss.<n>This framework generates closed-form predictive distributions over outputs with non-identically distributed and heteroscedastic structure.<n>We discuss its broader applicability to uncertainty-aware prediction in scientific models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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