A Biologically Constrained Continuous-Time Framework for Long-Horizon Cognition Forecasting in Alzheimer's Disease

Accurate long-term forecasting of cognitive trajectories across the Alzheimer's disease continuum is essential for early intervention, personalized prognosis, patient stratification, and clinical trial enrichment. Despite the promising predictive performance of recent longitudinal forecasting methods, they remain largely data-driven, struggle with irregularly sampled, incomplete longitudinal data and often neglect established disease biology, leading to biologically implausible trajectories. To address this, we propose a biologically constrained continuous-time framework for long-horizon cognition forecasting from limited baseline observations. The proposed method models the complete amyloid-tau-vascular-neurodegeneration-cognition (ATVNC) cascade using hierarchical Neural ODEs with biologically motivated monotonicity constraints. Each pathological stream is governed by a dedicated Neural ODE initialized from irregular longitudinal observations using a GRU-D encoder, capturing intrinsic disease evolution while being modulated by directed upstream pathological influences. A bounded cognition readout ensures physiologically valid cognitive score (MoCA) predictions, while teacher-student knowledge distillation improves learning from sparse longitudinal supervision. Evaluated on the ADNI dataset, the proposed framework achieves a long-horizon extrapolation MAE of 2.06 on 188 held-out participants while eliminating biologically implausible trajectory violations. It further demonstrates robust zero-shot cross-cohort generalization on OASIS-3 (MAE 2.68 on 300 participants), with fine-tuning improving MAE to 1.90. The model also supports prognostic enrichment for Alzheimer's clinical trials, achieving up to 2.70x enrichment over the cohort base rate. These results demonstrate that embedding biological disease mechanisms within continuous-time deep learning improves the accuracy, biological plausibility, and clinical utility of long-horizon cognitive forecasting. The code is publicly available at: https://github.com/PonDeepika/BEACON.