Physics‐Informed Fourier Neural Operator for Predicting the Full‐Field Stress and Strain Response of Polycrystalline Microstructures

ABSTRACT We develop a physics‐informed Fourier Neural Operator (PINO) for the surrogate modeling of full‐field responses in polycrystalline microstructures. Reference stress and strain fields are generated using an FFT‐based full‐field solver under prescribed macroscopic loading. The model maps the crystallographic orientation field and macroscopic strain to the strain fluctuation field and the stress field . The training objective combines supervised data losses with physics‐informed residuals. Specifically, local equilibrium is enforced using a stress‐divergence loss, while consistency with the FFT formulation is imposed through a Lippmann–Schwinger residual. An initial hyperparameter study shows how the relative weighting of these loss terms influences the predictive accuracy of the trained surrogate. Additionally, an adaptive weighting scheme is employed and compared with the fixed‐weight PINO. Both physics‐informed models are also compared with a purely data‐driven FNO to demonstrate the effect of incorporating physical constraints. The adaptive‐weight PINO achieves the lowest physical residual while retaining a data error comparable to the other training strategies. Furthermore, the model trained at a coarse resolution is evaluated without retraining at finer resolutions and at a macroscopic strain beyond the training range, demonstrating zero‐shot super‐resolution and load extrapolation.