Phase-field (PF) models are one of the most powerful tools to simulate microstructural evolution in metallic materials, polymers, and ceramics. However, existing PF approaches rely on rigorous mathematical model development, sophisticated numerical schemes, and high-performance computing for accuracy. Although recently developed surrogate microstructure models employ deep-learning techniques and reconstruction of microstructures from lower-dimensional data, their accuracy is fairly limited as spatio-temporal information is lost in the pursuit of dimensional reduction. Given these limitations, a novel data-driven emulator (DDE) for extrapolation prediction of microstructural evolution is presented, which combines an image-based convolutional and recurrent neural network (CRNN) with tensor decomposition, while leveraging previously obtained PF datasets for training. To assess the robustness of DDE, the emulation sequence and the scaling behavior with phase-field simulations for several noisy initial states are compared. In conclusion, the effectiveness of the microstructure emulation technique is explored in the context of accelerating runtime, along with an emphasis on its trade-off with accuracy.Meanwhile, an interpolation DDE has also been tested, which is based on obtaining a low-dimensional representation of the microstructures via tensor decomposition and subsequently predicting the microstructure evolution in the low-dimensional space using Gaussian process regression (GPR). Once the microstructure predictions are obtained in the low-dimensional space, a hybrid input-output phase retrieval algorithm will be employed to reconstruct the microstructures. As proof of concept, the results on microstructure prediction for spinodal decomposition are presented, although the method itself is agnostic of the material parameters. Results show that GPR-based DDE model are able to predict microstructure evolution sequences that closely resemble the true microstructures (average normalized mean square of 6.78 × 10−7) at time scales half of that employed in obtaining training data. This data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. Future work will also be discussed and demonstrate the intended utilization of these two approaches for 3D microstructure prediction through their combined application.