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Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) (https://github.com/ai2es/miles-guess), that enables users to train and evaluate both evidential and ensemble deep learning. Significance StatementThis study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.
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This content will become publicly available on December 13, 2025
Estimating Epistemic and Aleatoric Uncertainty with a Single Model
Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning to highstakes applications such as medical imaging and weather forecasting. Conditional diffusion models’ breakthrough ability to accurately and efficiently sample from the posterior distribution of a dataset now makes uncertainty estimation conceptually straightforward: One need only train and sample from a large ensemble of diffusion models. Unfortunately, training such an ensemble becomes computationally intractable as the complexity of the model architecture grows. In this work we introduce a new approach to ensembling, hyper-diffusion models (HyperDM), which allows one to accurately estimate both epistemic and aleatoric uncertainty with a single model. Unlike existing single-model uncertainty methods like Monte-Carlo dropout and Bayesian neural networks, HyperDM offers prediction accuracy on par with, and in some cases superior to, multi-model ensembles. Furthermore, our proposed approach scales to modern network architectures such as Attention U-Net and yields more accurate uncertainty estimates compared to existing methods. We validate our method on two distinct real-world tasks: x-ray computed tomography reconstruction and weather temperature forecasting. Source code is publicly available at https://github.com/matthewachan/hyperdm.
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- Award ID(s):
- 2425735
- PAR ID:
- 10614979
- Publisher / Repository:
- Curran Associates
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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