# Learning Absorption Rates in Glucose-Insulin Dynamics from Meal Covariates

arXiv: https://arxiv.org/abs/2304.14300 · HTML: https://mlsanity.com/paper/2304.14300/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Learning Latent Dynamics for Partially-Observed Chaotic Systems](https://mlsanity.com/paper/1907.02452/) (2019)
- [Breiman's two cultures: You don't have to choose sides](https://mlsanity.com/paper/2104.12219/) (2021)
- [Initializing LSTM internal states via manifold learning](https://mlsanity.com/paper/2104.13101/) (2021)
- [Enhancing Blood Glucose Prediction with Meal Absorption and Physical Exercise Information](https://mlsanity.com/paper/1901.07467/) (2018)

## Built on by (most cited first, 3 of 3)

- [GARNN: An Interpretable Graph Attentive Recurrent Neural Network for Predicting Blood Glucose Levels via Multivariate Time Series](https://mlsanity.com/paper/2402.16230/) (2024)
- [Structural Constraints for Physics-augmented Learning](https://mlsanity.com/paper/2410.05507/) (2024)
- [Interpretable Mechanistic Representations for Meal-level Glycemic Control in the Wild](https://mlsanity.com/paper/2312.03344/) (2023)

## Abstract (arXiv)

Traditional models of glucose-insulin dynamics rely on heuristic parameterizations chosen to fit observations within a laboratory setting. However, these models cannot describe glucose dynamics in daily life. One source of failure is in their descriptions of glucose absorption rates after meal events. A meal's macronutritional content has nuanced effects on the absorption profile, which is difficult to model mechanistically. In this paper, we propose to learn the effects of macronutrition content from glucose-insulin data and meal covariates. Given macronutrition information and meal times, we use a neural network to predict an individual's glucose absorption rate. We use this neural rate function as the control function in a differential equation of glucose dynamics, enabling end-to-end training. On simulated data, our approach is able to closely approximate true absorption rates, resulting in better forecast than heuristic parameterizations, despite only observing glucose, insulin, and macronutritional information. Our work readily generalizes to meal events with higher-dimensional covariates, such as images, setting the stage for glucose dynamics models that are personalized to each individual's daily life.