用几何框架统一建模可穿戴与环境数据，解析健康风险的动态演化机制。
Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams
- 将健康风险建模为时变单纯复形上的向量场，结合微分几何算子与多模态专家混合结构。
- 通过Hodge分解分离出驱动、循环和持久三种可解释的风险传播机制。
- 适合关注可解释性健康预测、多源异构数据融合的研究者。
数字健康研究已发展出基于动态图的疾病模型、单纯复形上的拓扑学习以及多模态专家混合架构，但这些方向仍彼此孤立。本文提出图向量场（GVF）框架，将健康风险建模为时变单纯复形上的向量值场，结合离散微分几何算子与结构化多模态专家混合机制。风险以向量值上链表示，其演化由Hodge拉普拉斯算子与离散外微分计算算子参数化，实现Helmholtz-Hodge分解，得到受势能驱动（精确）、环流类（共精确）和拓扑约束（调和）三部分，分别对应可解释的传播、周期性与持续性风险机制。可穿戴传感器、行为/环境上下文及临床/基因组数据通过纤维丛结构的专家混合模型融合，将各模态潜在空间作为纤维附着于基单纯复形，分离模态特异性与共享贡献，提供模态可识别性的理论路径。GVF将几何动力系统、高阶拓扑（通过几何正则化间接实现）与结构化多模态融合整合为统一框架，支持可解释、模态分辨的风险建模。本文构建数学基础、架构设计与形式保证；实证验证为后续工作。
原文摘要 · Abstract (English)
Digital health research has advanced dynamic graph-based disease models, topological learning on simplicial complexes, and multimodal mixture-of-experts architectures, but these strands remain largely disconnected. We propose Graph Vector Field (GVF), a framework that models health risk as a vector-valued field on time-varying simplicial complexes, coupling discrete differential-geometric operators with modality-structured mixture-of-experts. Risk is represented as a vector-valued cochain whose evolution is parameterised with Hodge Laplacians and discrete exterior calculus operators, yielding a Helmholtz-Hodge decomposition into potential-driven (exact), circulation-like (coexact), and topologically constrained (harmonic) components linked to interpretable propagation, cyclic, and persistent risk mechanisms. Multimodal inputs from wearable sensors, behavioural/environmental context, and clinical/genomic data are incorporated through a bundle-structured mixture-of-experts in which modality-specific latent spaces are attached as fibres to the base complex. This separates modality-specific from shared contributions and offers a principled route toward modality-level identifiability. GVF integrates geometric dynamical systems, higher-order topology (enforced indirectly via geometric regularisation and Hodge decomposition), and structured multimodal fusion into a single framework for interpretable, modality-resolved risk modelling. This paper develops the mathematical foundations, architectural design, and formal guarantees; empirical validation is the subject of ongoing work.
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