Abstract We will develop new large-scale dynamic models of manifold-valued data with a focus on dynamic symmetric positive de?nite (SPD) structures from nonstationary multivariate time series obtained from human functional magnetic resonance images (fMRI). The proposed new models and meth- ods will capture how functional brain connectivity dynamically changes over time and thus will be used to more accurately evaluate evolutionary dynamics of functional brain networks at the voxel level. We propose to build dynamically changing functional brain networks from a dataset with 1206 subjects from the Human Connectome Project (HCP) database containing T1-weighted magnetic resonance images (MRI), diffusion tensor images (DTI) and task and resting-state fMRI. MRI and DTI will be used in conjunction with fMRI in building more re?ned dynamic connectivity models. We will determine network phenotypes speci?c to behavior and their genetic associations. This study will provide the research community with the baseline brain network heritability maps as well as a versatile open-source toolbox of algorithms for modeling and visualizing dynamically changing large-scale brain networks.