Learning Difference Equations with Structured Grammatical Evolution for
  Postprandial Glycaemia Prediction
Daniel Parra David Joedicke J. Manuel Velasco Gabriel Kronberger J. Ignacio Hidalgo
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.