Identifying Differential Equations to predict Blood Glucose using Sparse Identification of Nonlinear Systems

Abstract: Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data is described. A combination of the influencing variables insulin and calories are used to find an interpretable model. The absorption speed of external substances in the human body depends strongly on external influences, which is why time-shifts are added for the influencing variables. The focus is put on identifying the best timeshifts that provide robust models with good prediction accuracy that are independent of other unknown external influences. The modeling is based purely on the measured data using Sparse Identification of Nonlinear Dynamics. A differential equation is determined which, starting from an initial value, simulates blood glucose dynamics. By applying the best model to test data, we can show that it is possible to simulate the long-term blood glucose dynamics using differential equations and few, influencing variables.