Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems
Uncertainty quantification (UQ) is critical for modeling complex dynamic systems, ensuring robustness and interpretability. This study extends Physics-Guided Bayesian Neural Networks (PG-BNNs) to enhance model robustness by integrating physical laws into Bayesian frameworks. Unlike Artificial Neural...
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MDPI AG
2025-02-01
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| author | Xinyue Xu Julian Wang |
| author_facet | Xinyue Xu Julian Wang |
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| collection | DOAJ |
| description | Uncertainty quantification (UQ) is critical for modeling complex dynamic systems, ensuring robustness and interpretability. This study extends Physics-Guided Bayesian Neural Networks (PG-BNNs) to enhance model robustness by integrating physical laws into Bayesian frameworks. Unlike Artificial Neural Networks (ANNs), which provide deterministic predictions, and Bayesian Neural Networks (BNNs), which handle uncertainty probabilistically but struggle with generalization under sparse and noisy data, PG-BNNs incorporate the laws of physics, such as governing equations and boundary conditions, to enforce physical consistency. This physics-guided approach improves generalization across different noise levels while reducing data dependency. The effectiveness of PG-BNNs is validated through a one-degree-of-freedom vibration system with multiple noise levels, serving as a representative case study to compare the performance of Monte Carlo (MC) dropout ANNs, BNNs, and PG-BNNs across interpolation and extrapolation domains. Model accuracy is assessed using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAE), and Coefficient of Variation of Root Mean Square Error (CVRMSE), while UQ is evaluated through 95% Credible Intervals (CIs), Mean Prediction Interval Width (MPIW), the Quality of Confidence Intervals (QCI), and Coverage Width-based Criterion (CWC). Results demonstrate that PG-BNNs can achieve high accuracy and good adherence to physical laws simultaneously, compared to MC dropout ANNs and BNNs, which confirms the potential of PG-BNNs in engineering applications related to dynamic systems. |
| format | Article |
| id | doaj-art-c77b9b5b9b6f4883aa91594a086a2de3 |
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| issn | 2571-9394 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-c77b9b5b9b6f4883aa91594a086a2de32025-08-20T02:11:17ZengMDPI AGForecasting2571-93942025-02-0171910.3390/forecast7010009Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic SystemsXinyue Xu0Julian Wang1Department of Architectural Engineering, Pennsylvania State University, State College, PA 16802, USADepartment of Architectural Engineering, Pennsylvania State University, State College, PA 16802, USAUncertainty quantification (UQ) is critical for modeling complex dynamic systems, ensuring robustness and interpretability. This study extends Physics-Guided Bayesian Neural Networks (PG-BNNs) to enhance model robustness by integrating physical laws into Bayesian frameworks. Unlike Artificial Neural Networks (ANNs), which provide deterministic predictions, and Bayesian Neural Networks (BNNs), which handle uncertainty probabilistically but struggle with generalization under sparse and noisy data, PG-BNNs incorporate the laws of physics, such as governing equations and boundary conditions, to enforce physical consistency. This physics-guided approach improves generalization across different noise levels while reducing data dependency. The effectiveness of PG-BNNs is validated through a one-degree-of-freedom vibration system with multiple noise levels, serving as a representative case study to compare the performance of Monte Carlo (MC) dropout ANNs, BNNs, and PG-BNNs across interpolation and extrapolation domains. Model accuracy is assessed using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAE), and Coefficient of Variation of Root Mean Square Error (CVRMSE), while UQ is evaluated through 95% Credible Intervals (CIs), Mean Prediction Interval Width (MPIW), the Quality of Confidence Intervals (QCI), and Coverage Width-based Criterion (CWC). Results demonstrate that PG-BNNs can achieve high accuracy and good adherence to physical laws simultaneously, compared to MC dropout ANNs and BNNs, which confirms the potential of PG-BNNs in engineering applications related to dynamic systems.https://www.mdpi.com/2571-9394/7/1/9uncertainty quantificationphysics-guided neural networkspredictive capabilityBayesian neural networkvibration dynamics |
| spellingShingle | Xinyue Xu Julian Wang Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems Forecasting uncertainty quantification physics-guided neural networks predictive capability Bayesian neural network vibration dynamics |
| title | Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems |
| title_full | Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems |
| title_fullStr | Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems |
| title_full_unstemmed | Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems |
| title_short | Comparative Analysis of Physics-Guided Bayesian Neural Networks for Uncertainty Quantification in Dynamic Systems |
| title_sort | comparative analysis of physics guided bayesian neural networks for uncertainty quantification in dynamic systems |
| topic | uncertainty quantification physics-guided neural networks predictive capability Bayesian neural network vibration dynamics |
| url | https://www.mdpi.com/2571-9394/7/1/9 |
| work_keys_str_mv | AT xinyuexu comparativeanalysisofphysicsguidedbayesianneuralnetworksforuncertaintyquantificationindynamicsystems AT julianwang comparativeanalysisofphysicsguidedbayesianneuralnetworksforuncertaintyquantificationindynamicsystems |