BrainODE: Neural Shape Dynamics for Age- and Disease-aware Brain Trajectories

We present BrainODE , a neural ordinary differential equation (ODE)-based framework for modeling continuous longitudinal deformations of brain shapes. BrainODE learns a deformation space over anatomically meaningful brain regions to facilitate early prediction of neurodegenerative disease progression. Addressing inherent challenges of longitudinal neuroimaging data—such as limited sample sizes, irregular temporal sampling, and substantial inter-subject variability—we propose a conditional neural ODE architecture that models shape dynamics with subject-specific age and cognitive status. To enable autoregressive forecasting of brain morphology from a single observation, we propose a pseudo-cognitive status embedding that allows progressive shape prediction across intermediate time points with predicted cognitive decline. Experiments show that BrainODE outperforms time-aware baselines in predicting future brain shapes, demonstrating strong generalization across longitudinal datasets with both regular and irregular time intervals.