Modelling CGM time series using Neural Ordinary Differential Equation

Abstract

According to a government survey(2019), 11.8% of people in India have diabetes. Understanding the glucose-insulin dynamics could help in designing clinical trials and help in designing therapies for prevention. There have been attempts to model the glucose-insulin dynamics as a step in that direction. Recently deep neural networks have been used to model a dynamic system. In our work, we take an existing dynamical system (Glucose- insulin) model and incorporate a simple neural network ( twice composed ReLu, with just two parameters). We show that this simple neural network (a piecewise linear term) can be used to approximate a non-linear term in the dynamical system. We introduce an algorithm to find the parameters of the neural network to fit the new dynamical system (with the neu- ral network) to the Continous Glucose Monitoring (CGM) data. The final results show that even after replacing the non-linear term with a piecewise linear function, the glucose-insulin time series obtained are close to the one obtained from the original glucose-insulin dynamics.