Prior-guided multi-fidelity deep learning for predicting stress intensity factors of semi-elliptical cracks

Data-driven surrogate models for fracture assessment are often constrained by the high computational cost of generating training data and the resulting data sparsity. To overcome these limitations, a prior-guided multi-fidelity (PG-MF) deep learning model is developed to predict the stress intensity factors (SIFs) of semi-elliptical cracks. Analytical solutions from fracture handbooks and simplified extended finite element method results serve as low- and intermediate-fidelity data, respectively. By learning the physical residuals between fidelity levels, results from the high-fidelity finite element method are accurately approximated even with severely limited training data. To ensure physical consistency, a B-spline output parameterization is employed where the neural network predicts control points rather than discrete values. An analytic domain mapping is introduced to enforce the zero-derivative symmetry condition at the deepest point of the crack as a hard-architectural constraint. A two-phase optimization strategy is adopted to prevent the degradation of the analytical prior by calibrating scaling parameters before refining residual networks. Deep ensemble-based uncertainty quantification is integrated to estimate epistemic uncertainty. The proposed model is validated on a cylindrical pressure vessel corner weld joint, where it is shown to outperform pure data-driven models. All prediction errors fall within the 2 σ confidence interval, even with a training set of only four high-fidelity samples. Furthermore, the model is coupled with the weight function method to directly calculate SIFs for arbitrary nonlinear stress distributions. This versatility confirms the capability of the model to support rapid structural integrity evaluations under diverse loading conditions.