Visualization of how the external stimuli are processed dynamically in the brain would help understanding the neural mechanisms of functional segregation and integration. The present study proposed a novel temporal autoencoder to estimate the neurodynamics of functional networks involved in rhythm encoding and reproduction. A fully-connected two-layer autoencoder was proposed to estimate the temporal dynamics in functional magnetic resonance image recordings. By minimizing the reconstruction error between the predicted next time sample and the corresponding ground truth next time sample, the system was trained to extract spatial patterns of functional network dynamics without any supervision effort. The results showed that the proposed model was able to extract the spatial patterns of task-related functional dynamics as well as the interactions between them. Our findings suggest that artificial neural networks would provide a useful tool to resolve temporal dynamics of neural processing in the human brain.