Learning Difference Equations with Structured Grammatical Evolution for Postprandial Glycaemia Prediction

TL;DR

This paper introduces an interpretable, grammar-based method for predicting post-meal blood glucose levels in diabetics, balancing accuracy with explainability to aid personalized treatment.

Contribution

It presents a novel grammatical evolution approach for generating interpretable difference equations for glucose prediction, improving safety and accuracy over existing methods.

Findings

Produces safe, explainable glucose predictions with minimal risk zones

Achieves slightly better accuracy than neural networks and sparse identification methods

Provides predictions with 15-minute resolution up to two hours post-meal

Abstract

People with diabetes must carefully monitor their blood glucose levels, especially after eating. Blood glucose regulation requires a proper combination of food intake and insulin boluses. Glucose prediction is vital to avoid dangerous post-meal complications in treating individuals with diabetes. Although traditional methods, such as artificial neural networks, have shown high accuracy rates, sometimes they are not suitable for developing personalised treatments by physicians due to their lack of interpretability. In this study, we propose a novel glucose prediction method emphasising interpretability: Interpretable Sparse Identification by Grammatical Evolution. Combined with a previous clustering stage, our approach provides finite difference equations to predict postprandial glucose levels up to two hours after meals. We divide the dataset into four-hour segments and perform clustering based on blood glucose values for the twohour window before the meal. Prediction models are trained for each cluster for the two-hour windows after meals, allowing predictions in 15-minute steps, yielding up to eight predictions at different time horizons. Prediction safety was evaluated based on Parkes Error Grid regions. Our technique produces safe predictions through explainable expressions, avoiding zones D (0.2% average) and E (0%) and reducing predictions on zone C (6.2%). In addition, our proposal has slightly better accuracy than other techniques, including sparse identification of non-linear dynamics and artificial neural networks. The results demonstrate that our proposal provides interpretable solutions without sacrificing prediction accuracy, offering a promising approach to glucose prediction in diabetes management that balances accuracy, interpretability, and computational efficiency.