In this talk, we propose a deep learning method for predicting the dynamics of the classic and conservative Allen-Cahn equations. We design two types of convolutional neural network models, one for each of the Allen-Cahn equations, to learn the fully-discrete operators between two adjacent time steps. Specifically, the loss functions of the two models are defined using the residual of the fully-discrete systems, which result from applying the central finite difference discretization in space and the Crank–Nicolson approximation in time (second-order accurate in both time and space). This approach enables us to train the models without requiring any ground-truth data. Moreover, we introduce a novel training strategy that automatically generates useful samples along the time evolution to facilitate effective training of the models. Finally, we conduct extensive experiments in two and three dimensions to demonstrate the outstanding performance of our proposed method, including its dynamics prediction and generalization ability under different scenarios.