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，预测变量的可靠不确定性量化对知情决策的重要性不容忽视。材料性能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、众多因素间的复杂交互作用、用于模型训练的大型精选数据集的有限可用性等。近年来，贝叶斯神经网络已成为不确定性量化领域的一种极具前景的方法，其通过概率框架捕捉神经网络中的不确定性。在本工作中，我们提出了一种融合物理知识的贝叶斯神经网络不确定性量化方法，该方法整合了材料建模中控制规律的知识，引导模型产生物理一致的预测。为评估该方法的有效性，我们以钢合金蠕变断裂寿命预测为案例展开研究。基于三组蠕变测试测量数据集的实验验证表明，贝叶斯神经网络能够产生精度与不确定性估计均具有竞争力的点预测结果，其性能可与传统高斯过程回归方法相媲美甚至超越后者。同时，我们在主动学习应用中评估了贝叶斯神经网络进行不确定性量化的适用性，并报告了其具有竞争力的性能。最具有前景的蠕变寿命预测框架是基于马尔可夫链蒙特卡洛近似网络参数后验分布的贝叶斯神经网络，因为相比于基于变分推断近似的贝叶斯神经网络或具有概率输出的相关神经网络，该框架提供了更可靠的结果。相关代码可访问：https://github.com/avakanski/Creep-uncertainty-quantification。