Fourier Neural Operator for Predicting the Growth of Precipitates in a Binary Alloy

Materials microstructural evolution can be effectively investigated with physics-based mod els, such as phase-field modeling. Nevertheless, the need to generate fine mesh systems in order to obtain numerical solutions of complex partial differential equations(PDEs) systems makes it compu tationally expensive. Therefore, the focus of this work is on Fourier Neural Operators (FNO), a quick and generalizable machine learning model that serves as a surrogate model. In this study, we have demonstrated the capability of FNO to learn the dynamics of precipitate growth. For interpolation settings, FNO could accurately predict the two coupled phase-field variables( c and η ) which represent the evolutionary state of the precipitate growth. It could also predict microstructure evolutions based on unseen initial conditions in extrapolation settings that is, outside the training set’s distribution of initial conditions. However, the error increases as we deviate further away from the distribution of the initial conditions used during training. For the case of precipitate growth in 1D with a system size of (X,T)=(4096*101), the Fourier neural operator has an inference time of only 0.027s compared to 0.21s of the pseudo-spectral method. We have also shown the capability of FNO in predicting the coupled phase-field variables at a higher resolution(4096*101) using the same model trained with low resolution data(64*101).