The phase-field method is a powerful and versatile computational approach for modeling the evolution of microstructures and associated properties for a wide variety of physical, chemical, and biological systems. However, existing high-fidelity phase-field models are inherently computationally expensive, requiring high-performance computing resources and sophisticated numerical integration schemes to achieve a useful degree of accuracy. In this paper, we present a computationally inexpensive, accurate, data-driven surrogate model that directly learns the microstructural evolution of targeted systems by combining phase-field and history-dependent machine-learning techniques. We integrate a statistically representative, low-dimensional description of the microstructure, obtained directly from phase-field simulations, with either a time-series multivariate adaptive regression splines autoregressive algorithm or a long short-term memory neural network. The neural-network-trained surrogate model shows the best performance and accurately predicts the nonlinear microstructure evolution of a two-phase mixture during spinodal decomposition in seconds, without the need for “on-the-fly” solutions of the phase-field equations of motion. We also show that the predictions from our machine-learned surrogate model can be fed directly as an input into a classical high-fidelity phase-field model in order to accelerate the high-fidelity phase-field simulations by leaping in time. Such machine-learned phase-field framework opens a promising path forward to use accelerated phase-field simulations for discovering, understanding, and predicting processing–microstructure–performance relationships.

Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost of 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 framework that integrates a convolutional autoencoder architecture with a deep neural operator (DeepONet) to learn the dynamic evolution of a two-phase mixture and accelerate time-to-solution in predicting the microstructure evolution. We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space. After DeepONet is trained in the latent space, it can be used to replace the high-fidelity phase-field numerical solver in interpolation tasks or to accelerate the numerical solver in extrapolation tasks.