发表机构
University of Notre Dame（圣母大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出可重训练的物理集成神经可微框架Sinter-PiNDiff，预测烧结中密度与晶粒尺寸演变，在多种材料上优于基线，支持稀疏数据预测与不确定性知情工艺选择。
AI 中文摘要
烧结广泛用于制造陶瓷，但致密化与晶粒生长的耦合、材料依赖的动力学特性以及稀疏的测量数据，使得预测建模和工艺设计变得复杂。我们提出了Sinter-PiNDiff，一种可重训练的物理集成神经可微框架，用于预测密度和晶粒尺寸的演变。两个神经网络在耦合的速率方程中学习致密化和晶粒生长系数，同时一个平滑饱和因子在接近理论密度时减弱致密化。相同的控制结构、网络架构和训练流程被独立地应用于MgO、Al掺杂ZnO和CaO掺杂ThO2的已发表数据。在留出的温度和成分测试中，与多层感知机和残差网络基线相比，在所有十二项材料-指标比较中取得了最低的平均误差。对于MgO、Al掺杂ZnO和CaO掺杂ThO2，密度归一化均方根误差分别为14.6%、10.8%和14.4%，使用相同指标的晶粒尺寸误差分别为8.6%、12.1%和19.3%。从两个神经网络输入中移除演变密度，导致所有三个体系中的密度和晶粒尺寸轨迹误差增加，并在十二项聚合误差中的十项中增加，支持了密度依赖的动力学反馈。深度集成估计了模型分歧，但经验覆盖表明不确定性带未经过校准，并未捕捉所有模型-数据差异。这些结果确立了Sinter-PiNDiff作为稀疏数据预测和不确定性知情选择烧结条件的可重训练框架。
英文摘要
Sintering is widely used to manufacture ceramics, but coupled densification and grain growth, material-dependent kinetics, and sparse measurements complicate predictive modeling and process design. We present Sinter-PiNDiff, a retrainable physics-integrated neural differentiable framework for predicting density and grain-size evolution. Two neural networks learn densification and grain-growth coefficients within coupled rate equations, while a smooth saturation factor attenuates densification near theoretical density. The same governing structure, network architecture, and training procedure were fitted independently to published data for MgO, Al-doped ZnO, and CaO-doped ThO2. Tests at held-out temperatures and compositions yielded the lowest mean error in all twelve material-metric comparisons against multilayer perceptron and residual network baselines. For MgO, Al-doped ZnO, and CaO-doped ThO2, respectively, density normalized root-mean-square errors were 14.6%, 10.8%, and 14.4%, and grain-size errors using the same metric were 8.6%, 12.1%, and 19.3%. Removing evolving density from both neural-network inputs increased density and grain-size trajectory errors in all three systems and ten of twelve aggregate errors, supporting density-dependent kinetic feedback. Deep ensembles estimated model disagreement, but empirical coverage showed that the uncertainty bands were not calibrated and did not capture all model-data discrepancies. These results establish Sinter-PiNDiff as a retrainable framework for sparse-data prediction and uncertainty-informed selection of sintering conditions.
