Physics-Informed Neural Koopman Machine for Interpretable Longitudinal Personalized Alzheimer's Disease Forecasting

TL;DR

This paper introduces the Neural Koopman Machine, a novel interpretable deep learning framework that leverages dynamical systems and attention mechanisms to improve personalized, multimodal forecasting of cognitive decline in Alzheimer's disease.

Contribution

The Neural Koopman Machine integrates analytical and biological knowledge within a Koopman operator framework to enhance interpretability and accuracy in longitudinal AD forecasting.

Findings

Outperforms traditional and deep learning models in forecasting cognitive decline.

Simultaneously predicts multiple cognitive scores with high accuracy.

Identifies key biomarkers and brain regions associated with AD progression.

Abstract

Early forecasting of individual cognitive decline in Alzheimer's disease (AD) is central to disease evaluation and management. Despite advances, it is as of yet challenging for existing methodological frameworks to integrate multimodal data for longitudinal personalized forecasting while maintaining interpretability. To address this gap, we present the Neural Koopman Machine (NKM), a new machine learning architecture inspired by dynamical systems and attention mechanisms, designed to forecast multiple cognitive scores simultaneously using multimodal genetic, neuroimaging, proteomic, and demographic data. NKM integrates analytical ($\alpha$) and biological ($\beta$) knowledge to guide feature grouping and control the hierarchical attention mechanisms to extract relevant patterns. By implementing Fusion Group-Aware Hierarchical Attention within the Koopman operator framework, NKM transforms complex nonlinear trajectories into interpretable linear representations. To demonstrate NKM's efficacy, we applied it to study the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Our results suggest that NKM consistently outperforms both traditional machine learning methods and deep learning models in forecasting trajectories of cognitive decline. Specifically, NKM (1) forecasts changes of multiple cognitive scores simultaneously, (2) quantifies differential biomarker contributions to predicting distinctive cognitive scores, and (3) identifies brain regions most predictive of cognitive deterioration. Together, NKM advances personalized, interpretable forecasting of future cognitive decline in AD using past multimodal data through an explainable, explicit system and reveals potential multimodal biological underpinnings of AD progression.