Graph Vector Field: A Unified Framework for Multimodal Health Risk Assessment from Heterogeneous Wearable and Environmental Data Streams

Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of physical, engineered, and data-driven systems. The objective of this work is to establish a unified perspective on such systems, to identify modeling approaches that balance expressivity, interpretability, computational complexity, and data requirements, and to investigate how highly expressive models can be used to uncover the dominant mechanisms underlying observed dynamics. Starting from the Helmholtz-Hodge decomposition of continuous vector fields, we review the recently proposed Graph Vector Field (GVF) framework and its discrete representation on simplicial complexes. We then introduce a hierarchy of alternative approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations. Finally, we propose a verification and validation methodology based on benchmark datasets from well-understood physical systems and on systematic model-reduction and ablation studies. The resulting family of structured-flow models within a common framework, ranging from low-dimensional parametric representations to full GVF formulations, supports a diagnostic methodology in which gradient, curl, harmonic, and topological contributions are systematically assessed through ablation studies. This process enables the identification of dominant mechanisms underlying the observed dynamics and guides the construction of simplified models tailored to the available data and operational constraints. By separating structural verification, behavioral verification, and domain-specific validation, the proposed approach provides a foundation for scalable and interpretable analysis of complex dynamical systems across multiple application domains.

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around latent, risk-factor-modulated disease pathways. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.

Estimating heat-related mortality risk is a core task in environmental epidemiology, typically addressed with Distributed Lag Non-linear Models (DLNMs); interpretable exposure-response surfaces fitted to temperature-mortality time series. DLNMs are effective but ignore demographic and geographic context, despite well-established relevance to heat vulnerability. We propose Risk Graph Neural Networks (RGNNs), a hierarchical GNN encoder that uses granular census features to optimise DLNM coefficient vectors, preserving interpretable risk curve outputs while substantially improving predictive calibration. Evaluated across 10 regions of England and Wales on two unprecedented heat years, RGNN variants maintain both lower point-errors and near-nominal uncertainty coverage during the 2022 heatwave where baselines collapse.