Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning
This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or heteroscedasticity. Unlike traditional neural networks that produ...
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| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10771767/ |
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| author | Farhad Pourkamali-Anaraki Jamal F. Husseini Scott E. Stapleton |
| author_facet | Farhad Pourkamali-Anaraki Jamal F. Husseini Scott E. Stapleton |
| author_sort | Farhad Pourkamali-Anaraki |
| collection | DOAJ |
| description | This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or heteroscedasticity. Unlike traditional neural networks that produce deterministic outputs, PNNs generate probability distributions for the target variable, allowing the determination of both predicted means and variances in regression scenarios. Contributions of this paper include the development of a probabilistic distance metric to optimize PNN architecture, and the deployment of PNNs in controlled data sets as well as a practical material science case involving fiber-reinforced composites. The findings confirm that PNNs effectively model aleatoric uncertainty, proving to be more appropriate than the commonly employed Gaussian process regression for this purpose. Specifically, in a real-world scientific machine learning context, PNNs yield remarkably accurate output mean estimates with R-squared scores approaching 0.97, and their predicted variances exhibit a high correlation coefficient of nearly 0.77, closely matching observed data variances. Hence, this research contributes to the ongoing exploration of leveraging the sophisticated representational capacity of neural networks to delineate complex input-output relationships in scientific problems. |
| format | Article |
| id | doaj-art-0bacf2bb71724e739fe8fb0c7c7a34d8 |
| institution | OA Journals |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-0bacf2bb71724e739fe8fb0c7c7a34d82025-08-20T02:33:48ZengIEEEIEEE Access2169-35362024-01-011217881617883110.1109/ACCESS.2024.350873510771767Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine LearningFarhad Pourkamali-Anaraki0https://orcid.org/0000-0003-4078-1676Jamal F. Husseini1Scott E. Stapleton2Department of Mathematical and Statistical Sciences, University of Colorado at Denver, Denver, CO, USADepartment of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USADepartment of Mechanical and Industrial Engineering, University of Massachusetts at Lowell, Lowell, MA, USAThis paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or heteroscedasticity. Unlike traditional neural networks that produce deterministic outputs, PNNs generate probability distributions for the target variable, allowing the determination of both predicted means and variances in regression scenarios. Contributions of this paper include the development of a probabilistic distance metric to optimize PNN architecture, and the deployment of PNNs in controlled data sets as well as a practical material science case involving fiber-reinforced composites. The findings confirm that PNNs effectively model aleatoric uncertainty, proving to be more appropriate than the commonly employed Gaussian process regression for this purpose. Specifically, in a real-world scientific machine learning context, PNNs yield remarkably accurate output mean estimates with R-squared scores approaching 0.97, and their predicted variances exhibit a high correlation coefficient of nearly 0.77, closely matching observed data variances. Hence, this research contributes to the ongoing exploration of leveraging the sophisticated representational capacity of neural networks to delineate complex input-output relationships in scientific problems.https://ieeexplore.ieee.org/document/10771767/Probabilistic neural networksaleatoric uncertaintyprediction intervalnetwork architecture optimization |
| spellingShingle | Farhad Pourkamali-Anaraki Jamal F. Husseini Scott E. Stapleton Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning IEEE Access Probabilistic neural networks aleatoric uncertainty prediction interval network architecture optimization |
| title | Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning |
| title_full | Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning |
| title_fullStr | Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning |
| title_full_unstemmed | Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning |
| title_short | Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning |
| title_sort | probabilistic neural networks pnns for modeling aleatoric uncertainty in scientific machine learning |
| topic | Probabilistic neural networks aleatoric uncertainty prediction interval network architecture optimization |
| url | https://ieeexplore.ieee.org/document/10771767/ |
| work_keys_str_mv | AT farhadpourkamalianaraki probabilisticneuralnetworkspnnsformodelingaleatoricuncertaintyinscientificmachinelearning AT jamalfhusseini probabilisticneuralnetworkspnnsformodelingaleatoricuncertaintyinscientificmachinelearning AT scottestapleton probabilisticneuralnetworkspnnsformodelingaleatoricuncertaintyinscientificmachinelearning |