A process-aligned convolutional framework for cross-resolution phase-field prediction in adaptive mesh refinement simulations of brittle fracture

Phase-field fracture models offer a robust way to simulate crack initiation, propagation, branching, and coalescence without explicit tracking. However, accurate results demand highly refined meshes to resolve steep damage gradients. Even with adaptive mesh refinement (AMR), simulations remain computationally heavy because each refinement step requires solving nonlinear finite element systems at increasingly finer resolutions. In this paper, we introduce a novel data-driven alternative that learns the refinement behavior directly, eliminating the need to run the finest adaptive refined simulations. Specifically, we develop a multi-resolution learning framework that uses hierarchical mesh data and a process-aligned fracture coordinate to train a neural network capable of predicting fine-mesh phase-field solutions from those of successive coarser meshes. Unlike previous approaches, which typically downsample fine solutions or learn temporal dynamics, our approach learns the forward refinement map itself, enabling it to act as a surrogate for AMR. The model conditions its internal representation on the stage of fracture, concentrates attention in regions where refinement is physically needed, and reconstructs high-resolution fields through a stable log-domain update rule. Applied to single-edge notched tension and shear tests, it recovers crack paths, interface sharpness, and progression with normalized errors below 0.3%. Training completes in under one minute on CPU, and inference is instantaneous, providing adaptive fine-mesh accuracy at a tiny fraction of the computational cost. These results offer a practical route to fine-mesh accuracy at a fraction of the traditional computational cost, bridging the long-standing gap between computational efficiency and solution accuracy.