The intrinsic activity of the brain is organized into networks and motifs that vary over time. To understand how coordinated macroscale patterns of intrinsic activity flow across the brain’s structural network, new analysis approaches that can extract interpretable spatial and temporal features are required. We demonstrate the use of machine learning to extract prototypical spatiotemporal trajectories of brain activity that provide a sparse and elegant basis of representation. To better interpret the spatiotemporal patterns of brain activity, we incorporate brain network models as constraints, forcing the algorithm to learn parameters that can be measured empirically. This interpretable machine learning-based approach paves the way for multimodal experiments that can validate or disprove the accuracy of different brain network models.