DevelopmentODE: Structured Neural ODEs for Early Brain Development Dynamics Across a Decade

Understanding how individual brain development unfolds over childhood requires modeling developmental trajectories from sparse longitudinal observations. Long-term neurodevelopmental forecasting is not simply extending short-term prediction to longer horizons as each child is typically observed at only a few irregularly spaced visits and developmental dynamics vary substantially with individuals and age. Generic continuous-time models naturally accommodate irregular timing, but typically absorb these sources of variation into a single flexible transition function, providing little structure for how population-level progression, individual variability, and developmental age should shape the dynamics. We propose DevelopmentODE, a structured continuous-time framework that organizes population and subject-specific variation within a shared developmental geometry while allowing the governing dynamics to evolve with developmental age. The model establishes this geometry around a developmental canal representing the population-level trajectory, whose local direction provides a reference for organizing subject-specific variation. Subject deviation velocities are constrained relative to this developmental direction, while a shared nonlinear deviation field captures individual developmental motion without disrupting population-level progression. Building on the same geometry, DevelopmentODE captures developmental non-stationarity through ordered age-dependent deformations of the shared vector field. These deformations progressively adapt a common underlying dynamical structure as developmental age changes, while elapsed time determines how long the resulting dynamics are integrated. The resulting formulation leverages broadly supported population-level developmental structure to guide learning from sparse individual trajectories, while allowing the governing dynamics to evolve smoothly across developmental age. We evaluate DevelopmentODE on longitudinal fMRI data by predicting future functional connectivity observations of the same child from earlier developmental observations. DevelopmentODE consistently outperforms competing baselines across short- and long-horizon predictions. These results support the benefit of explicitly structuring developmental dynamics for long-horizon neurodevelopmental forecasting.