Channel prediction is critical to address the channel aging issue in mobile scenarios. Existing channel prediction techniques are mainly designed for discrete channel prediction

which can only predict the future channel in a fixed time slot per frame

while the other intra-frame channels are usually recovered by interpolation. However

these approaches suffer from a serious interpolation loss

especially for mobile millimeter-wave communications. To solve this challenging problem

we propose a tensor neural ordinary differential equation (TN-ODE) based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels. Specifically

inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning

we first utilize the neural ODE model to predict future continuous-time channels. To improve the channel prediction accuracy and reduce computational complexity

we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform. Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes.