标题： 用物理信息变分自编码器混合模型学习神经退行性机制亚型 显示英文标题

标题： Learning Mechanistic Subtypes of Neurodegeneration with a Physics-Informed Variational Autoencoder Mixture Model

摘要： 建模神经退行性疾病的潜在机制需要能够从稀疏的高维神经成像数据中捕捉异质性和空间变化动态的方法。 将基于偏微分方程（PDE）的物理知识与机器学习相结合，相较于经典数值方法提供了更高的可解释性和实用性。 然而，当前集成物理的机器学习方法仅限于考虑单一的PDE，严重限制了其在多种机制导致不同组别（即亚型）的疾病中的应用，并加剧了模型误设和退化问题。 在此，我们提出了一种深度生成模型，用于学习由基于物理的PDE控制的潜在动态模型的混合，超越了传统方法假设单一PDE结构的局限。 我们的方法在变分自编码器（VAE）混合模型框架内集成了反应扩散PDE，支持从神经成像数据中推断可解释的潜在变量亚型（例如扩散率和反应速率）。 我们在合成基准上评估了我们的方法，并展示了其从正电子发射断层扫描（PET）数据中揭示阿尔茨海默病进展的机制亚型的潜力。 显示英文摘要

摘要： 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.