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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.16686 |
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| _version_ | 1866911117386711040 |
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| author | Goldwyn, Harrison J. Krock, Mitchell Rudi, Johann Getter, Daniel Bessac, Julie |
| author_facet | Goldwyn, Harrison J. Krock, Mitchell Rudi, Johann Getter, Daniel Bessac, Julie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed Goldwyn, Harrison J. Krock, Mitchell Rudi, Johann Getter, Daniel Bessac, Julie Machine Learning Methodology 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. |
| title | Multidimensional Distributional Neural Network Output Demonstrated in Super-Resolution of Surface Wind Speed |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2508.16686 |