HKD-MGIN: a physics informed graph neural network using heat kernel diffusion for mapping adolescent functional brain connectivity.

Adolescence is a critical period characterized by dynamic changes in cognitive function and brain network organization. This study aims to model these complex neurodevelopmental processes using a novel graph-based learning framework that captures both local and global functional interactions across adolescent stages. We introduce the Heat Kernel Diffused Multi-task Graph Isomorphism Network (HKD-MGIN), which integrates multi-task functional magnetic resonance imaging (fMRI) data using heat kernel diffusion. This approach leverages a graph isomorphism network architecture to enable robust and interpretable representation learning. HKD-MGIN is applied to two predictive tasks: brain age estimation and sex classification. HKD-MGIN demonstrated strong performance in brain age estimation (RMSE = 1.864 ± 0.157; MAE = 1.492 ± 0.139; r = 0.816 ± 0.042) and achieved high accuracy in sex classification (ACC = 0.802 ± 0.015; AUC = 0.834 ± 0.017; F1 Score = 0.8199 ± 0.0514). Importantly, the model revealed functional circuits associated with cognitive maturation, highlighting its capacity for interpretability and neurobiological insight. These findings demonstrate the utility of heat kernel-based graph learning in modeling adolescent brain dynamics and identifying potential biomarkers of cognitive development. HKD-MGIN advances neuroimaging analysis by capturing hierarchical and distributed connectivity patterns, offering a promising direction for individualized tracking of neurodevelopmental trajectories.