Learning two-phase microstructure evolution using neural operators and autoencoder architectures

Phase-field modeling is an effective mesoscale method for capturing the evolution dynamics of materials, e.g., in spinodal decomposition of a two-phase mixture. However, the accuracy of high-fidelity phase field models comes at a substantial computational cost. Hence, fast and generalizable surrogate models are needed to alleviate the cost in computationally taxing processes such as in optimization and design of materials. The intrinsic discontinuous nature of the physical phenomena incurred by the presence of sharp phase boundaries makes the training of the surrogate model cumbersome. We develop a new framework that integrates a convolutional autoencoder architecture with a deep neural operator (DeepONet) to learn the dynamic evolution of a two-phase mixture. We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space. DeepONet, which consists of two sub-networks, one for encoding the input function at a fixed number of sensors locations (branch net) and another for encoding the locations for the output functions (trunk net), learns the mesoscale dynamics of the microstructure evolution in the latent space. The decoder part of the convolutional autoencoder can then reconstruct the time-evolved microstructure from the DeepONet predictions. The result is an efficient and accurate accelerated phase-field framework that outperforms other neural-network-based approaches while at the same time being robust to noisy inputs.