# Neural operator-based digital twins for modeling amyloid-β and tau propagation and treatment optimization in Alzheimer's disease

arXiv: https://arxiv.org/abs/2606.25185 · HTML: https://mlsanity.com/paper/2606.25185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression](https://mlsanity.com/paper/2307.08107/) (2023)
- [Optimal Control For Anti-Abeta Treatment in Alzheimer's Disease using a Reaction-Diffusion Model](https://mlsanity.com/paper/2504.07913/) (2025)
- [Data-Driven Modeling of Spatiotemporal Dynamics Using Multimodal Imaging Data](https://mlsanity.com/paper/2511.08847/) (2025)

## Abstract (arXiv)

Accurately predicting the spatiotemporal evolution of amyloid-β and tau proteins at the individual level is critical for improving the diagnosis and treatment of Alzheimer's disease. We consider the problem of constructing patient-specific digital twins that model the propagation of these biomarkers on the cortical surface using reaction--diffusion dynamics. A major challenge is that the underlying nonlinear aggregation mechanisms are unknown and must be inferred from sparse, noisy, and heterogeneous longitudinal PET imaging data. To address this, we develop a data-driven framework that learns biomarker dynamics directly from clinical observations. The approach combines operator learning with reduced-order representations to infer governing equations of disease progression from data. Using this framework, we achieve predictive accuracies of 87% for amyloid-β and 81% for tau. Building on the learned dynamics, we further formulate a PDE-constrained optimal control problem to design personalized therapeutic strategies that regulate pathological protein propagation. By integrating data-driven dynamical modeling with treatment optimization, the proposed digital twin framework provides an interpretable and predictive platform for understanding disease progression and enabling precision interventions in neurodegenerative disorders.