Scalable dynamical inference of phase-field fracture from sparse and partial measurements

Abstract

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.