  With the increased use of data-driven approaches and machine learning-based
methods in material science, the importance of reliable uncertainty
quantification (UQ) of the predicted variables for informed decision-making
cannot be overstated. UQ in material property prediction poses unique
challenges, including the multi-scale and multi-physics nature of advanced
materials, intricate interactions between numerous factors, limited
availability of large curated datasets for model training, etc. Recently,
Bayesian Neural Networks (BNNs) have emerged as a promising approach for UQ,
offering a probabilistic framework for capturing uncertainties within neural
networks. In this work, we introduce an approach for UQ within physics-informed
BNNs, which integrates knowledge from governing laws in material modeling to
guide the models toward physically consistent predictions. To evaluate the
effectiveness of this approach, we present case studies for predicting the
creep rupture life of steel alloys. Experimental validation with three datasets
of collected measurements from creep tests demonstrates the ability of BNNs to
produce accurate point and uncertainty estimates that are competitive or exceed
the performance of the conventional method of Gaussian Process Regression.
Similarly, we evaluated the suitability of BNNs for UQ in an active learning
application and reported competitive performance. The most promising framework
for creep life prediction is BNNs based on Markov Chain Monte Carlo
approximation of the posterior distribution of network parameters, as it
provided more reliable results in comparison to BNNs based on variational
inference approximation or related NNs with probabilistic outputs. The codes
are available at:
https://github.com/avakanski/Creep-uncertainty-quantification.
