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

2025-12-05

AI Summary

Early, interpretable longitudinal prediction of individualized cognitive decline in Alzheimer’s disease (AD) remains challenged by the difficulty of jointly achieving effective multimodal data fusion and model transparency. To address this, we propose the Neural Koopman Machine (NKM), a physics-informed, group-aware hierarchical attention framework that integrates genetic, neuroimaging, proteomic, and demographic data. NKM maps nonlinear cognitive trajectories onto interpretable linear Koopman representations, enabling simultaneous prediction of multidimensional cognitive scores and quantification of biomarker-specific contributions. Model architecture is constrained by two priors: α-prior (analytical prior) guiding feature organization and β-prior (biological prior) governing dynamic modeling. Evaluated on the ADNI dataset, NKM significantly outperforms state-of-the-art machine learning and deep learning baselines. It further identifies neuroanatomically and biologically salient predictive regions and biomarkers, offering a clinically actionable, mechanistically insightful tool for AD research and decision support.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Multi-modal Vision

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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 ($α$) and biological ($β$) 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.

Problem

• Forecasts cognitive decline in Alzheimer's using multimodal data
• Integrates interpretability into personalized longitudinal disease forecasting
• Transforms complex patient trajectories into linear interpretable representations

Innovation

• Uses Neural Koopman Machine with attention for multimodal data forecasting
• Transforms nonlinear trajectories into interpretable linear representations
• Integrates analytical and biological knowledge to guide feature grouping