The neural dynamics underlying brain activity are critical to understanding cognitive processes and mental disorders. However, current voxel-based whole-brain dimensionality reduction techniques fail to capture these dynamics, producing latent timeseries that inadequately relate to behavioral tasks. To address this issue, we introduce a novel approach to learning low-dimensional approximations of neural dynamics using a sequential variational autoencoder (SVAE) that learns the latent dynamical system. Importantly, our method finds smooth dynamics that can predict cognitive processes with accuracy higher than classical methods, with improved spatial localization to task-relevant brain regions, and we find fixed points for the dynamics that are stable across random initialization of the model.