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

arXiv: https://arxiv.org/abs/2603.28115 · HTML: https://mlsanity.com/paper/2603.28115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [GRAM: Graph-based Attention Model for Healthcare Representation Learning](https://mlsanity.com/paper/1611.07012/) (2016)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Deep Learning in Human Activity Recognition with Wearable Sensors: A Review on Advances](https://mlsanity.com/paper/2111.00418/) (2021)
- [Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks](https://mlsanity.com/paper/1703.02161/) (2017)
- [Bundle Neural Networks for message diffusion on graphs](https://mlsanity.com/paper/2405.15540/) (2024)
- [Learning Dynamic and Personalized Comorbidity Networks from Event Data using Deep Diffusion Processes](https://mlsanity.com/paper/2001.02585/) (2020)
- [MoE-Health: A Mixture of Experts Framework for Robust Multimodal Healthcare Prediction](https://mlsanity.com/paper/2508.21793/) (2025)
- [Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps](https://mlsanity.com/paper/2203.08189/) (2022)
- [Adaptive Geometric Regression for High-Dimensional Structured Data](https://mlsanity.com/paper/2511.03817/) (2025)
- [Learning Longitudinal Health Representations from EHR and Wearable Data](https://mlsanity.com/paper/2601.12227/) (2026)

## Built on by (most cited first, 1 of 1)

- [A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery](https://mlsanity.com/paper/2605.18250/) (2026)

## Abstract (arXiv)

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.