# Learning Patient-Specific Spatial Biomarker Dynamics via Operator Learning for Alzheimer's Disease Progression

arXiv: https://arxiv.org/abs/2507.16148 · HTML: https://mlsanity.com/paper/2507.16148/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2025.

## Abstract (arXiv)

Alzheimer's disease (AD) is a complex, multifactorial neurodegenerative disorder with substantial heterogeneity in progression and treatment response. Despite recent therapeutic advances, predictive models capable of accurately forecasting individualized disease trajectories remain limited. Here, we present a machine learning-based operator learning framework for personalized modeling of AD progression, integrating longitudinal multimodal imaging, biomarker, and clinical data. Unlike conventional models with prespecified dynamics, our approach directly learns patient-specific disease operators governing the spatiotemporal evolution of amyloid, tau, and neurodegeneration biomarkers. Using Laplacian eigenfunction bases, we construct geometry-aware neural operators capable of capturing complex brain dynamics. Embedded within a digital twin paradigm, the framework enables individualized predictions, simulation of therapeutic interventions, and in silico clinical trials. Applied to AD clinical data, our method achieves high prediction accuracy exceeding 90% across multiple biomarkers, substantially outperforming existing approaches. This work offers a scalable, interpretable platform for precision modeling and personalized therapeutic optimization in neurodegenerative diseases.