Exploring Efficient Quantification of Modeling Uncertainties with Differentiable Physics-Informed Machine Learning Architectures
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916838842040320 |
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| author | Oddiraju, Manaswin Penumatsa, Bharath Varma Amin, Divyang Piedmonte, Michael Chowdhury, Souma |
| author_facet | Oddiraju, Manaswin Penumatsa, Bharath Varma Amin, Divyang Piedmonte, Michael Chowdhury, Souma |
| contents | Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML) methods have emerged in recent years as a new alternative to traditional computational modeling and surrogate modeling methods, offering a balance between computing efficiency, modeling accuracy, and interpretability. However, their ability to predict and propagate modeling uncertainties remains mostly unexplored. In this paper, a promising class of auto-differentiable hybrid PIML architectures that combine partial physics and neural networks or ANNs (for input transformation or adaptive parameter estimation) is integrated with Bayesian Neural networks (replacing the ANNs); this is done with the goal to explore whether BNNs can successfully provision uncertainty propagation capabilities in the PIML architectures as well, further supported by the auto-differentiability of these architectures. A two-stage training process is used to alleviate the challenges traditionally encountered in training probabilistic ML models. The resulting BNN-integrated PIML architecture is evaluated on an analytical benchmark problem and flight experiments data for a fixed-wing RC aircraft, with prediction performance observed to be slightly worse or at par with purely data-driven ML and original PIML models. Moreover, Monte Carlo sampling of probabilistic BNN weights was found to be most effective in propagating uncertainty in the BNN-integrated PIML architectures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Efficient Quantification of Modeling Uncertainties with Differentiable Physics-Informed Machine Learning Architectures Oddiraju, Manaswin Penumatsa, Bharath Varma Amin, Divyang Piedmonte, Michael Chowdhury, Souma Machine Learning Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML) methods have emerged in recent years as a new alternative to traditional computational modeling and surrogate modeling methods, offering a balance between computing efficiency, modeling accuracy, and interpretability. However, their ability to predict and propagate modeling uncertainties remains mostly unexplored. In this paper, a promising class of auto-differentiable hybrid PIML architectures that combine partial physics and neural networks or ANNs (for input transformation or adaptive parameter estimation) is integrated with Bayesian Neural networks (replacing the ANNs); this is done with the goal to explore whether BNNs can successfully provision uncertainty propagation capabilities in the PIML architectures as well, further supported by the auto-differentiability of these architectures. A two-stage training process is used to alleviate the challenges traditionally encountered in training probabilistic ML models. The resulting BNN-integrated PIML architecture is evaluated on an analytical benchmark problem and flight experiments data for a fixed-wing RC aircraft, with prediction performance observed to be slightly worse or at par with purely data-driven ML and original PIML models. Moreover, Monte Carlo sampling of probabilistic BNN weights was found to be most effective in propagating uncertainty in the BNN-integrated PIML architectures. |
| title | Exploring Efficient Quantification of Modeling Uncertainties with Differentiable Physics-Informed Machine Learning Architectures |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.18247 |