Data-based uncertainty quantification plays a significant role in the design of various patterns of new materials and structures. However, significant challenges remain due to missing data, inherent uncertainties, and incomplete material properties arising from the manufacturing process. In this paper, we quantitatively investigate the uncertainty in the probability of the mechanical response of bio-inspired porous structures, specifically focusing on a RotTPMS plate as input data in the current study. Practicality, datasets can be collected from arbitrary material sources such as open-access libraries, experimental data, or numerical simulation results. Initially, machine learning models were utilized to handle incomplete data on metal material properties through imputation. The imputation methods used for filling in the data include MEAN, KNN, MICE, GAIN, and MISSFOREST. The results showed that the MISSFOREST method was the most accurate, with the lowest MAPE values of 3.19% for Es, 0.66% for νs, and 2.6% for ρs. Concurrently, we introduce an efficient BNN-pSGLD model, which employs Bayesian neural networks with the preconditioned stochastic gradient Langevin dynamics method for sampling and optimization, aimed at data-driven uncertainty quantification. A data-driven computational framework, named Material-UQ, is proposed to probabilistically predict the mechanical response of various structures, accounting for uncertainties in material properties. The BNN-pSGLD model achieves higher R2 performance than conventional machine learning models such as ANNs, Decision Trees, and Random Forests. Additionally, to assist designers in accurately predicting and managing uncertainties in material and structural design, detailed discussions and deep explanations of the uncertainty in the present approach are also conducted.

中文翻译：

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概率仿生多孔材料中的数据驱动不确定性量化框架 （Material-UQ）：RotTMPS 板的研究


基于数据的不确定性量化在各种新材料和结构模式的设计中发挥着重要作用。然而，由于制造过程中出现的数据缺失、固有的不确定性和不完整的材料特性，仍然存在重大挑战。在本文中，我们定量研究了仿生多孔结构机械响应概率的不确定性，特别关注 RotTPMS 板作为当前研究的输入数据。实用性，可以从任意材料来源收集数据集，例如开放访问库、实验数据或数值仿真结果。最初，机器学习模型用于通过插补处理有关金属材料特性的不完整数据。用于填充数据的插补方法包括 MEAN、KNN、MICE、GAIN 和 MISSFOREST。结果表明，MISSFOREST 方法最准确，Es 的 MAPE 值最低，为 3.19%，νs 为 0.66%，ρs 为 2.6%。同时，我们引入了一个高效的 BNN-pSGLD 模型，该模型采用贝叶斯神经网络和预条件随机梯度 Langevin 动力学方法进行采样和优化，旨在实现数据驱动的不确定性量化。提出了一个名为 Material-UQ 的数据驱动计算框架，用于概率预测各种结构的机械响应，并考虑材料特性的不确定性。BNN-pSGLD 模型实现了比传统机器学习模型（如 ANN、决策树和随机森林）更高的 R2 性能。 此外，为了帮助设计人员准确预测和管理材料和结构设计中的不确定性，还对当前方法中的不确定性进行了详细讨论和深入解释。