Verification of Bayesian Physics-Informed Neural Networks

With the rapid advancement of machine learning technology, its applications are becoming increasingly vital across various critical systems and domains. However, the effectiveness of machine learning models heavily depends on high-quality data, which is often costly to obtain and affected by inherent uncertainty. To address this challenge, we propose a robust Bayesian physics-informed neural network (BPINN) that enables the analysis of limited datasets while incorporating uncertainty quantification, all while maintaining the physical interpretability of predictions. In this study, we develop a verification problem to systematically assess and verified the effectiveness and robustness of our approach and shown the performance by predicting the fracture time of a steel alloy based on very limited dataset.

Keywords: Machine learning, Uncertainty quantification, Benchmark problems, Bayesian physics-informed neural networks.