用物理模型混合生成神经退行性疾病亚型，提升机制可解释性。
Learning Mechanistic Subtypes of Neurodegeneration with a Physics-Informed Variational Autoencoder Mixture Model
- 基于反应-扩散方程构建变分自编码器混合模型，捕捉多机制动态
- 从PET数据中识别出阿尔茨海默病的多个可解释亚型，如扩散率差异
- 适合神经科学与医学图像分析研究者，尤其关注疾病异质性建模
神经退行性疾病机制建模需要能够从稀疏、高维神经影像数据中捕捉异质性和空间变化动态的方法。将偏微分方程（PDE）物理知识与机器学习结合，比传统数值方法更具可解释性和实用性。然而，现有物理融合机器学习方法仅限于单一PDE，严重限制了在多机制驱动疾病亚型中的应用，并加剧模型误设和退化问题。本文提出一种深度生成模型，用于学习由物理驱动的多个潜在动态模型的混合结构，突破传统假设单一生理过程的局限。该方法将反应-扩散型PDE嵌入变分自编码器（VAE）混合框架，支持从神经影像数据中推断可解释的潜变量亚型（如扩散率、反应速率）。我们在合成基准上评估方法性能，并展示其在正电子发射断层扫描（PET）数据中揭示阿尔茨海默病进展机制亚型的潜力。
原文摘要 · Abstract (English)
Modelling the underlying mechanisms of neurodegenerative diseases demands methods that capture heterogeneous and spatially varying dynamics from sparse, high-dimensional neuroimaging data. Integrating partial differential equation (PDE) based physics knowledge with machine learning provides enhanced interpretability and utility over classic numerical methods. However, current physics-integrated machine learning methods are limited to considering a single PDE, severely limiting their application to diseases where multiple mechanisms are responsible for different groups (i.e., subtypes) and aggravating problems with model misspecification and degeneracy. Here, we present a deep generative model for learning mixtures of latent dynamic models governed by physics-based PDEs, going beyond traditional approaches that assume a single PDE structure. Our method integrates reaction-diffusion PDEs within a variational autoencoder (VAE) mixture model framework, supporting inference of subtypes of interpretable latent variables (e.g. diffusivity and reaction rates) from neuroimaging data. We evaluate our method on synthetic benchmarks and demonstrate its potential for uncovering mechanistic subtypes of Alzheimer's disease progression from positron emission tomography (PET) data.
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