The connection patterns of brain networks form a complex and dynamic network. By observing the alteration of these networks over time, one can detect brain disorders. Recent studies have demonstrated the potential to predict the evolution of brain networks from a single observation using graph neural networks (GNNs). This capability allows for the early-stage diagnosis of brain diseases, helping to prevent them from progressing into more severe conditions such as Alzheimer’s disease. However, none of the existing research has explored the potential of generating brain connectomes while preserving their cognitive capacity (e.g., memory capacity). All existing GNN models are cognition-agnostic. In this paper, we aim to address this gap in the literature by proposing our novel Dynamic Graph Neural Network model (DynGNN), the first framework that combines graph neural networks endowed with a dynamic memorisation task. To achieve this, we leverage the reservoir computing paradigm, alongside our novel loss function which matches the memory capacity of the predicted connectomes with the actual memory capacity observed in the ground truth data over time. We benchmarked the DynGNN model against various GNN models and datasets. Our results demonstrate that DynGNN models outperform others in generating temporal brain connectivities that closely align with actual memory functions. Furthermore, the DynGNN models exhibited fewer topological errors compared to their non-memory-enhanced counterparts, thereby further preserving the brain topology. Our DynGNN code is available at https://github.com/basiralab/DynGNN .