Parametric phase-field brittle fracture computations with convolutional Fourier neural operators

Abstract The variational phase-field approach to fracture has emerged as a powerful framework for modeling complex fracture phenomena, yet in the computational setting its reliance on discretizations that resolve small length scales makes it very expensive for parametric studies and real-time applications. In this paper, we propose the use of the Convolutional Fourier neural operator (C-FNO)—a data-driven operator learning architecture that enhances the global spectral capabilities of Fourier neural operators (FNOs) with local spatial convolutions—to surrogate phase-field brittle fracture simulations. We evaluate the performance of the C-FNO on two-dimensional single-edge notched specimens under varying geometric (initial notch length) and loading (magnitude and angle) parameters. Our results demonstrate that the C-FNO accurately predicts crack propagation, kinking, and branching across unseen parameter combinations, achieving very low mean absolute errors with a training time of a few hours and an inference time of the order of ten seconds. Notably, the addition of local convolution layers allows the model to capture nearly sharp cracks that are typically smoothed out by vanilla FNOs. This work highlights the potential of operator learning frameworks to provide high-fidelity, high-speed predictions for computational fracture mechanics.