基于稀疏局部测量的相场断裂可扩展动力学推断
Scalable dynamical inference of phase-field fracture from sparse and partial measurements
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中文总结 AI 辅助
开发CNN2D--ConvGRU卷积循环框架，可从稀疏测量高效重建全场相场脆性断裂状态，在精度与计算成本间取得平衡，CPU加速175倍、GPU加速253倍。
中文摘要 AI 辅助
结构健康监测与断裂评估中，扩展的裂纹场常需从稀疏力学测量而非密集全场观测中推断。我们开发了CNN2D--ConvGRU，一种用于测量条件下时变相场脆性断裂重建的卷积循环框架。在每个加载步，模型将相场与位移场的固定长度历史，以及稀疏当前步位移测量，映射为当前全场状态。序列部署过程中会同化新测量，使该框架成为状态推断代理而非自主时间积分器。它能复现裂纹路径、损伤演化及整体位移响应，最大误差出现在扩展裂纹尖端与陡峭位移梯度附近，后期存在一定漂移。未重新训练的情况下，在256×256栅格上学习到的权重，可在相同物理域、有限元离散化的512×512栅格上评估，采用按比例细化的测量网格。这种经验性栅格与传感迁移保留了主要损伤拓扑与全局损伤演化，尽管裂纹尖端附近细尺度位移误差增加。与其他时空架构的比较显示，CNN2D--ConvGRU在重建精度与计算成本间取得了良好平衡。相较于重复有限元求解，序列重建在CPU上实现了175倍的平均加速，在GPU上实现了253倍的平均加速。这些结果证明，可从稀疏观测中高效重建全场断裂状态，同时保留相场断裂的空间结构与历史依赖性。
英文摘要
Evolving crack fields in structural health monitoring and fracture assessment must often be inferred from sparse mechanical measurements rather than dense full-field observations. We develop CNN2D--ConvGRU, a convolutional-recurrent framework for measurement-conditioned reconstruction of time-dependent phase-field brittle fracture. At each load step, the model maps a fixed-length history of phase and displacement fields and sparse current-step displacement measurements to the current full-field state. New measurements are assimilated during sequential deployment, making the framework a state-inference surrogate rather than an autonomous time integrator. It reproduces crack paths, damage evolution, and bulk displacement response, with the largest errors near propagating crack tips and steep displacement gradients and some drift at late stages. Without retraining, weights learned on a $256 \times 256$ raster are evaluated on a $512 \times 512$ raster of the same physical domain and finite-element discretization using a proportionally refined measurement grid. This empirical raster-and-sensing transfer preserves the principal damage topology and global damage evolution, although fine-scale displacement errors increase near crack tips. Comparisons with alternative spatial and temporal architectures show that CNN2D--ConvGRU offers a favorable balance between reconstruction accuracy and computational cost. Relative to repeated finite-element solutions, sequential reconstruction achieves mean speedups of $175\times$ on CPU and $253\times$ on GPU. These results demonstrate efficient full-field fracture-state reconstruction from sparse observations while retaining the spatial structure and history dependence of phase-field fracture.
