The discovery of resting-state networks has greatly influenced the investigation of brain functioning, shifting the focus from local regions involved in cognitive tasks to the ongoing spontaneous dynamics in global networks. This research goes beyond that shift and proposes investigating how human cognition is shaped by the interactions between whole-brain networks embedded in a low-dimensional manifold space. To achieve this, a combination of deep variational autoencoders with computational modelling is used to construct a dynamic model of brain networks, fitted to whole-brain dynamics measured with functional magnetic resonance imaging (fMRI). The results show that during cognitive tasks, highly flexible reconfigurations of task-driven network interaction patterns occur, and these patterns, in turn, can be used to accurately classify different cognitive tasks. Importantly, using this low-dimensional whole-brain network model provides significantly better results than working in the conventional brain space.