用变分神经网络量化材料微结构不确定性，提升数字孪生可靠性。
Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins
- 在物理驱动的层级架构中嵌入变分分布，捕捉微结构变异
- 基于泰勒展开与自动微分，高效传播不确定性，支持正反向预测
- 适用于增材制造复合材料性能预测与多源不确定性分离
随机不确定性——微结构形貌、组分行为和加工条件中无法消除的变异——严重制约了高鲁棒性材料数字孪生的发展。本文提出变分深度材料网络（VDMN），一种融合物理信息的代理模型，可实现材料行为的高效概率化正向与反向预测。VDMN通过在其分层机制架构中嵌入变分分布，捕捉由微结构引起的变异性。利用基于泰勒级数展开与自动微分的解析传播方案，VDMN在训练和预测阶段均能高效传播不确定性。我们展示了其在两类数字孪生驱动应用中的能力：(1) 作为不确定性感知的材料数字孪生，成功预测并实验验证了增材制造聚合物复合材料的非线性力学变异性；(2) 作为逆向标定引擎，可解耦并定量识别重叠的组分属性不确定性来源。这些结果确立了VDMN作为不确定性鲁棒材料数字孪生的基础框架。
原文摘要 · Abstract (English)
Aleatoric uncertainties - irremovable variability in microstructure morphology, constituent behavior, and processing conditions - pose a major challenge to developing uncertainty-robust digital twins. We introduce the Variational Deep Material Network (VDMN), a physics-informed surrogate model that enables efficient and probabilistic forward and inverse predictions of material behavior. The VDMN captures microstructure-induced variability by embedding variational distributions within its hierarchical, mechanistic architecture. Using an analytic propagation scheme based on Taylor-series expansion and automatic differentiation, the VDMN efficiently propagates uncertainty through the network during training and prediction. We demonstrate its capabilities in two digital-twin-driven applications: (1) as an uncertainty-aware materials digital twin, it predicts and experimentally validates the nonlinear mechanical variability in additively manufactured polymer composites; and (2) as an inverse calibration engine, it disentangles and quantitatively identifies overlapping sources of uncertainty in constituent properties. Together, these results establish the VDMN as a foundation for uncertainty-robust materials digital twins.
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