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 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.