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.

翻译：随着数据驱动方法和基于机器学习的方法在材料科学中的广泛应用，可靠的不确定性量化对于支持明智决策的重要性不言而喻。材料属性预测中的不确定性量化面临独特挑战，包括先进材料的多尺度与多物理特性、众多因素之间的复杂相互作用、可用于模型训练的大型精选数据集有限等。近年来，贝叶斯神经网络作为一种前景广阔的不确定性量化方法崭露头角，提供了在神经网络中捕捉不确定性的概率框架。本研究提出一种融入物理信息的贝叶斯神经网络不确定性量化方法，该方法整合材料建模中控制规律的知识，引导模型做出符合物理规律的预测。为评估该方法的有效性，我们通过预测钢合金蠕变断裂寿命的案例研究进行验证。基于三个蠕变测试实验测量数据集的实验验证表明，贝叶斯神经网络能够产生精确的点估计和不确定性估计，其性能与高斯过程回归传统方法相当甚至更优。同样，我们在主动学习应用中评估了贝叶斯神经网络用于不确定性量化的适用性，并报告了具有竞争力的性能。基于网络参数后验分布的马尔可夫链蒙特卡洛近似的贝叶斯神经网络被证明是最有前景的蠕变寿命预测框架，与基于变分推断近似或具有概率输出的相关神经网络相比，该框架提供了更可靠的结果。代码可通过以下链接获取：https://github.com/avakanski/Creep-uncertainty-quantification。